Exercise 8.1 in trigonometry typically refers to the exercises in Chapter 8 of the NCERT Class 10 Maths textbook.


Here are the solutions to Exercise 8.1:


Exercise 8.1

1. In ΔABC, right-angled at B, AB = 24 cm, BC = 7 cm. Find:

1.1 sin A
1.2 cos A
1.3 tan A

Solution:

1.1 sin A = opposite side / hypotenuse = BC / AC = 7 / 25
1.2 cos A = adjacent side / hypotenuse = AB / AC = 24 / 25
1.3 tan A = opposite side / adjacent side = BC / AB = 7 / 24


2. In ΔPQR, right-angled at Q, PQ = 12 cm, QR = 5 cm. Find:

2.1 sin P
2.2 cos P
2.3 tan P

Solution:

2.1 sin P = opposite side / hypotenuse = QR / PR = 5 / 13
2.2 cos P = adjacent side / hypotenuse = PQ / PR = 12 / 13
2.3 tan P = opposite side / adjacent side = QR / PQ = 5 / 12


3. If sin A = 3/5, find cos A and tan A.

Solution:

Using sin²A + cos²A = 1,
cos A = √(1 - sin²A) = √(1 - (3/5)²) = 4/5
tan A = sin A / cos A = 3/4


4. If cos A = 4/5, find sin A and tan A.

Solution:

Using sin²A + cos²A = 1,
sin A = √(1 - cos²A) = √(1 - (4/5)²) = 3/5
tan A = sin A / cos A = 3/4


5. If tan A = 7/24, find sin A and cos A.

Solution:

Using tan A = sin A / cos A,
sin A = tan A / √(1 + tan²A) = 7 / 25
cos A = 1 / √(1 + tan²A) = 24 / 25


Please let me know if you'd like me to clarify or expand on any of these solutions.


Additional Resources:

1. NCERT Class 10 Maths textbook
2. Online tutorials and videos
3. Practice worksheets and exercises #class10 #trigonometry #cbse #math