B.Sc. Trigonometry (B.Sc notes)(B.Sc notes)
191 videos • 4,628 views • by Master of Mathematics
(B.Sc notes)(B.Sc notes)
1
7/1*3*5+19/5*7*9+31/9*11*13+...........find the sum of the series
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2
if tanha=cosθ ; prove thata=log (cotθ+cosecθ)
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3
Separate real and imaginary parts of Tan-1 (cosθ+isinθ)
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4
sin-1(cosθ+isinθ)
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5
Relation betbeen inverse hyperbolic functions and inverse circular functions
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6
B.Sc.I math trigonometry exponential and hyperbolic functions
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7
Relation between hyperbolic and circular functions
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8
B.Sc. Mathematics:cos (a+ib) Separate real and imaginary parts.
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9
if w=t.sinθ+t^2.sin2θ+t^3.sin3θ+...... prove that sinw=t.sin (w+θ)
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10
prove that cot-(3-2i/3+2i=π/4+i×log5/2)
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11
tan-1 (x)/x+tan-1 (y)/y+tan-1 (z)/z=3 [1-1/7+1/13-1/19+1/25-.....
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12
B.Sc. Mathematics :cosh(x)-cosh (y)=2sinh(x+y/2) .sinh (x-y/2) (prove that)
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13
if sin (a+ib)=tanθ+isecθ prove that cos2θ.cosh2θ=3
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14
if sin-1 (u+iv)=a+ib;then prove that sin^2a and cosh^2b are the roots of the equation part1/2
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15
if x is acute y=log [tan (π/4+x/2)] prove that cos(x).cosh (y)=1
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16
if sin (x+iy)=(5_/7+i9)/16,prove that one of the value of x+iy is cos-1 (3/4)+i.log2
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17
Expand (1-2x.cosθ+x^2)^-1
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18
Expand tanθ in terms of θ.
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19
B.Sc. Mathematics:separate real and imaginary part of Sin-1 (x+iy)
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20
B.Sc. Mathematics:separate real and imaginary part of Sin-1 (x+iy)
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21
2sinh (A).sinh (B)=cosh (A+B)-cosh (A-B)
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22
prove that if (1+itana)^(1+itann can have real values one of them is (seca)^sec^2b
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23
prove thatsinh (x)+sinh(y)=2sinh(x+y/2).cosh (x-y/2)
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24
prove that x^i=e^-2n(π)[cos{log(x)}+sin {log(x)}]
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25
tan-1 [(x+iy)/(x+iy)]=π/4+i/2log [(x+iy)/(x-iy)]
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26
if i^a+ib=a+ibshow that a^2+b^=e^-(4n+1)pi.b
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27
cos (a+ib).cos (α+iβ)=1prove that tanh^2(b).cosh^2 (β)=sin^2 (α)
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28
If cos-1(α+iβ)=θ+iφ prove that α^2/cosh^2φ+β^2/sinh^2φ=1 and α^2/cos^2θ-β^2/sin^2θ=1.
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29
B.Sc. Mathematics :(x+iy)=? separate into real and imaginary parts
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30
cosθ-1/3cos3θ+1/5cos5θ-...... (find the sum of series)Gregory series
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31
tan[log (x+iy)]=a+ib
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32
cos-1 (i) separate real and imaginary parts
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33
Coshx=secθ prove that(i )u=log (secθ+tanθ)(ii) x=log [tan (45+θ/2)]
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34
B.Sc. Mathematics:separate real and imaginary parts of log [sin (θ+iΦ)]
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35
(B) [sin^2(x+y)] resolve into real and imaginary parts
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36
y=-i×log[tan(x/2+pi/4)]
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37
e^iθ/1-ce^ia Separate into Real and imaginary part of
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38
math B.Sc.I inverse circular function of complex quantities
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39
[sin(a+θ)-e^ia.sinθ]^n=sin^a.e^(-inθ)
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40
B.Sc. Mathematics:Gregory series proof (Trigonometry)
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41
B.Sc. Mathematics:Question based on Gregory series in hindi/urdu
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42
B.Sc. Mathematics:sum of Sine series with angles in arthimatics progration(AP)
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43
trigonometry exponential problems
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44
Trigonometry cos hyperbolic related problems
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45
trigonometry hyperbolic related problems
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46
trigonometry exponential problem
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47
Prove that cos(α+iβ)+isin(α+iβ)=e^-β(cosα+isinα)
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48
If coshα=cosθ,prove that tanh^2α/2=tan^2θ/2
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49
If cosh(u+iv)=x+iy prove that x^2/cos^2v-y^2/sin^2v=1and x^2/cosh^2u+y^2/sinh^2u=1
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50
If sin(α+iβ)=x+iy;prove that (i)x^2cosec^2α-y^2sec^2β=1.(ii)x^2sech^2α+y^2cosech^2β=1
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51
1-1/3-1/5+1/7+1/9-........=1/_/2.log (_/2+1)
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52
Logi (i)=4m+1/4n+1 where m and n are intrgers (prove that )
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53
(x+ix.tany)^[log (xlogy)-iy]
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54
B.Sc.mathematics :Trigonometry : Sinh-1 (z)=log [z+_/z^2+1]
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55
To prove tanh-1 (z)=1/2log [(1+z)/(1-z)]
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56
cosθ/1*2-cos2θ/2*3+cos3θ/3*4-........
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57
sinθ.sin3θ+sinθ/2.sin3θ/2+sin@/2^2.sib3θ/2^2+......up to n terms
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58
[sin (a+θ)-e^a.i*sinθ]^n=e^(-nθ).sin^n (a)
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59
B.Sc.mathematics:trigonometry : tanh3x=3tanhx+tanh^3x/1+3tanh^2x
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60
log (-5)
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61
tan-1 (x)=x^2-1/2 (1+1/3)x^4+1/3 (1+1/3+1/5)x^6-......
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62
π/4=17/21-713/81×343+...... +(-1)^n+1/(2n-1)[2/3*9^1-n+7^1-2n]
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63
(a+ib)^i in form of A+iB
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64
If cos^-1 (u+iv)=a+ib;prove that cos^2a and cosh^2b are the roots of the equation x^2-x (1+u^2+v^2)+
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65
Log [log (i)]
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66
i^i^i=cosθ+i.sinθ prove that θ=()π.e^()
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67
B.-125:B.Sc. Mathematics :^2$.cos (θ+b)=cos (θ-b)
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68
solve:(1)sinhx=1(2)coshx=1/-/2(3)tanh=-/3(4)tanhx=0.75
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69
sigma from 1 to m cos^n(@).cos (n@)
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70
B.Sc. Mathematics :1/2 (coshx+cox)=1+x^4/4!+x^8/8!+......
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71
B.Sc. Mathematics :1/2 (coshx+cox)=1+x^4/4!+x^8/8!+......
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72
Log(i)=1/2 (2n+1/2)*π
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73
If tan(x+iy)=α+iβ than prove that α/sin2x=β/sinh2y= 1/(cos2x+cosh2y)
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74
1/2.sin^2θ=2tan^2θ-4tan^4θ+6tan^6-.... (if θ less than π/4
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75
if sin-1 (x+iy)=tan-1 (u+iy)than prove that [(x2+y2)/(u^2+v^2)]^2=[(x+1)^2+y2][(x-1)2+y2]
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76
To prove 1/1^2+1/2^2+1/3^2+........=π^2/6
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77
summation of series
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78
π/12=(1-1/√3)-1/3(1-1/√3^3)+1/5(1-1/√3^5)+..…..
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79
B.Sc. Mathematics:prove that:log(x+iy)=1/2log(x^2+y2)+tan-1(y/x)
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80
a Gregory series problem (watch at 360p )
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81
Cos(-z)=cos(z). Prove that
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82
Find the sum of the following series cot-1 (2^2+1/2)+cot(2^3+1/2^2)+cot(2^4+1/2^3)+......
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83
B.Sc. Mathematics : If u=log [tan (π/4+θ/2)] ,prove that tanh (u/2)=tan (θ/2)
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84
B.Sc.Mathematics:Expand cosx in ascending power of x.
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85
part -3 कुरान और साँइसIron miracle part3
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86
B.Sc.Mathematics:1-xcos@+x^2.cos2@-........up to n term (sum the series)
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87
B.Sc. Mathematics :Trigonometry:To Express sin(θ) as an infinite product
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88
B.Sc. Mathematics:Coth(x+iy) into real and imaginary parts
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89
B.Sc. Mathematics : Tanh(x+iy) separate into real and imaginary parts
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90
B.Sc.Math:Log{cos (x+iy)} separate into real and imaginary parts trigonometry
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91
Express cosθ as an infinite product
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92
B.Sc. Mathematics: Sum of cosine series of angle in AP
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93
[A]1+c.cos@+c^2.cos2@+...... where c is less than one numerically (sum to n terms of infinite serie
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94
B.Sc. Mathematics:e^sin (x+iy) separate real and imaginary parts
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95
B.Sc. Mathematics:prove that tan (@1+@2+@3+........@n)=(S1-S3+S5-..........)/(1-S2+S4-S6+......)
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96
B.Sc. Trigonometry:Express exp. [loga+ib] into x+iy
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97
B.Sc. :Matrices:Show following system of equations are inconsistentx+y+z=-33x+y-2z=-22x+4y+7z=7
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98
B.Sc.Mathematics Put (a+be^i@) in form of A+iB
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99
B.Sc I trigonometry exponential hyperbolic related problem 8
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100
B.Sc.Itrigonometry exponential hyperbolic related problem
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101
B.Sc.I Mathtrigonometry exponential hyperbolic related problems
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102
B.Sc.l trigonometry: exponential hyperbolic related problem
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103
math B.Sc.I trigonometry exponential hyperbolic related problem
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104
tan(@+i$)=tana+iseca then prove that e^i$=
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105
B.Sc. I trigonometry logarithm of complex function
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106
B.Sc. maths:Trigonometry:logarithm of complex quantity:(trigonometry).
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107
B.Sc.I math:part IIlogarithm of complex quantity: trigonometry:
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108
B.Sc.I :Logarithmic question {trigonometry}
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109
B.Sc.I mathLogarithm question 2#trigonometry#
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110
B.Sc. I ; trigonometry
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111
B.Sc. I Logarithm problem trigonometry
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112
B.Sc. Mathematics:tan(x+iy)To separate into real and imaginary parts ofTan(x+iy)
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113
Complex trigonometry:B.Sc.I honour
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114
Expansion of sin(alfa) in ascending power of alfa by use of De Moiver theorem
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115
Prove that 16 Sin^5(θ)=sin5θ-5.sin3θ+10.sinθ
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116
Sinh (x+iy) separate real and imaginary parts
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117
e^cosh (x+iy) separate into real and imaginary parts
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118
prove that sinh (a/2)=tan@
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119
Find the sum of the following series: 7/1.3.5+19/5.7.9+31/9.11.13+........ ad inf.
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120
If sin(x+iy).sin(θ+iϕ)=1,show that (i)tanh^2(y).coth^2(ϕ)=cos^2(θ (ii)tanh^2(ϕ).cosh(y)=cos^2(x)
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121
tan-1(1+cosθ/1-cosθ)=n.π+π/4+tanθ_1/3tan^3θ+....
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122
If cosh-1(x+iy)+cosh-1(x-iy)=cosh-1(a) prove that 2(a-1)x^2+2(a+1)y^2=a^2-1
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123
38 A:1-1/3*4^2+1/5*4^4-..........=4tan-1 (1/4)
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124
1+xcos@+x^2.cos2@+.............up to n terms :trigonometry:summation of series
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125
n.pi+pi/4+tan@-1/3tan^3@+1/5tan^5@-.....
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126
e^(ib)/(1-c.e^ia)
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127
Log i base i=(4n+1/2)/(4m+1/2)
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128
Prove that (1+coshx+sinhx)^n=2^n.coshx/2(coshnx/2+sinhnx/2)
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129
Show that cosπ/7,cos3π/7,cos5π/7 are roots of the equation 8x^3-4x^2-4x+1=0 and deduce the equation
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130
Show that cosπ/7,cos3π/7,cos5π/7 are roots of the equation 8x^3-4x^2-4x+1=0 and deduce the equation
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131
Show that cosπ/7,cos3π/7,cos5π/7 are roots of the equation 8x^3-4x^2-4x+1=0 and deduce the equation
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132
Show that cosπ/7,cos3π/7,cos5π/7 are roots of the equation 8x^3-4x^2-4x+1=0 and deduce the equation
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133
1-2cosa+3cos2a-4cos3a+......... to n terms
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134
1-2cosa+3cos2a-4cos3a+......... to n terms
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135
1-2cosa+3cos2a-4cos3a+......... to n terms
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136
If cosA+i.sinA=cos(θ+i.phi),prove that sin^2θ=+-sinA sinh^2(phi)=sinA
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137
If x lies between -π/4 and +π/4,show that tanx-1/3tan^3(x)+1/5tan^5(x)-........=tanh(x)+1/3tanh^3(
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138
Find real and imaginary parts of cosh-1(x+iy)
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139
logc=loga-b/a.cosC-B.Sc. Trigonometry summation of series:
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140
cosec(a-ib) Resolve into real and imaginary parts:Trigonometry:B.Sc. Mathematics
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141
1/3-1/3.1/3^3+1/5.1/3^5-.......=tan-1(1/3)
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142
cosθ-1/2.cos2θ+1/3.cos3θ-....Find the sum
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143
Show that the sum of moduli of the values of (1+i)^(1+i),which are less than unity is 1/-/2.e^3pi/4.
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144
If u= log[tan(π/4+θ/2)],prove that θ=-i.log[tan(π/4+iu/2)]
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145
Show that tan[ilog(a-ib)/(a+ib)]=2ab/(a^2-b^2)
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146
If sin(θ+i$)=tan(a)+isec(a ) then prove that cos2θ.cosh2$=3
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147
If cos(A+iB).cos(x+iy)=1; prove that tan(A).tanh(B)=tanh(x).tan(y)
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148
The general value of log(-2) base 4.
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149
Show that one of the values of log[(1+i)(1+i_/3)/(_/3+i)] is 1/2log2+i.5pi/12
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150
if cos(x+iy)=cosa+i.sina,then prove that cosh2y+cos2y=2
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151
i^i^i separate real and imaginary parts
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152
Express cosh-1(x+iy) into real and imaginary parts
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153
Separate into real and imaginary parts of cot(x+it)
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154
Express tan-1(x+iy) as the sum of real and imaginary parts
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155
Separate into real and imaginary parts of tanh(x+iy)
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156
Separate (1+i)^log(1+i) into real and imaginaryvparts
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157
part- 2 iron miracle of quran
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158
Separate into real and imaginary parts e^iψ/1-c.e^ϕ
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159
#25December Jesus Christ in holy Quran(Miracle of Quran)
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160
Separate real and imaginary parts tan(α+iβ) :B.Sc. Mathematics
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161
If u=logtan(π/4+x/2)=x+a3x^3+a5x^5+.prove that x=u-a3u^3+a5u^5-.. Top mathematics channel on YouTube
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162
Separate into real and Imaginary parta:sin-1(x+iy)
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163
π/2=logi/i
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164
tan-1 (sec@)=
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165
If coshx=secθ,prove that iθ=logtan(π/4+ix/2).
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166
If tan(x+iy)=u+iv,prove that (1-u^2-v^2)cosh2y=(1+u^2+v^2)cos2x #trigonometry
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167
Separate into real and imaginary parts cothi(x+iy)
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168
What is the value of (e^iπ/2)^3
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169
If sinα+sinβ+sinγ =cosα+cosβ+cosγ =0,prove that sin2α+sin2β+sin2γ =cos3α+cos2β+cos2γ =0 and sin^2α+s
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170
Separate into real and imaginary parts of expression cot(α-iβ).
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171
If tan(A+iB)=x+iy, prove that x^2+y^2+2xcot2A=1 and x^2+y^2-2ycot2A+1=0. #b.s.c.trigonometry
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172
Express log[log(cosx+isinx)] in the form A+iB. #B.Sc.Trigonometry
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173
(Reharsal video) Miracle of Quran.For Dawah purpose
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174
If u=logtan(π/4+θ/2),prove that tanhu/2=tanθ/2
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175
If A,B,C are angles of a triangle prove that |e^2iA e-iC e^-iB; e^-| is purely real.Find its value.
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176
If cos(x+iy)=cosα+isinα,prove that sinh^4y=sin^2α
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177
Find the general value of log(-i).
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178
Prove that tan(iloga-ib/a+ib)=2ab/a^2-b^2
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179
Prove that i^i=e^-(4n+1)π/2
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180
B.Sc. Mathematics :r=xi+yj+zk then find div.grad (1/r)
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181
If tan(A+iB)=x+iy prove that (1)tan2A=2x/1-x^2-y^2(2) tanh2B=2y/1+x^2+y^2
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182
log [log {cosθ+isinθ}]
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183
Prove that [sin(α+θ)-e^iα.sinθ]^n=sin^n(α).e^niθ
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184
Use De Moivre's theorem to solve equation x^7+x^4+x^3+1=0.
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185
If u=logtan(π/4+θ/2),prove that coshu=secθ.
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186
separate into real and imaginary parts of cos(α+iβ)
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187
If sin(x+iy)=A+iB,prove that A^2/cosh^2y+B^2/sinh^2y=1 and A^2/sin^2x-B^2/cos^2x=1.
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188
Find the principle and general value of log(-1+i).
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189
If tan(A+iB)=x+it, prove that x^2+y^2+2xcot2A=1 and x^2+y^2-2ycoth2B=-1.
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190
Reduce tan-1(cosθ+sinθ) to the form a+ib hence show that tan-1(e^iθ)=nπ/2+π/4+i/2logtan(π/4+θ/2).
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191
If tanθ=tanhxcoty and tanϕ=tanhxtany , prove that sin2θ/sin2ϕ=(cosh2x+cos2y)/(cosh2x-cos2y)
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