Simplify cos(2arcos(x)) and graph it. #maths #olympiad #calculus

We're going to talk about inverse. Trigonometric functions. We Define the cosine, the sign And the tangent, the arctangent, the r cosine, and the arc sine, And we're gonna study them, We're going to use the half angle formula To make sure that we get these functions when we compose by these functions. We're most of the time we get polynomials So we're going to be careful when we have the composite of function and its inverse. So, in our case, we're gonna study what we mean by these functions, what's an inverse function of a trigonometic trigonometric function, What's its domain? How can we find its domain? What's its range? When we talk about a function like the tangent of the arctangent of X, What's that value? How can we determine the value? How can we determine the range? And how can we determine the domain? In this case, how can we work with this functions? We will prove all these results when we have time. So in our case, this is the best place where you can learn about Treconometric functions and inverse trigonometric functions. This is the best channel on YouTube, where you can find all the information that you need about radians degrees trigonometric functions. Sign the cosine, the tangent, the accurate engine, the arc tangent, and all those values. We're gonna graph them and solve the equations relating to these ones. Solving equations is very important in dealing with techonometric functions. That's what we're gonna do. Here Is very important to us. That's why we A p c calculus. It's very important to us. That's why we're gonna do a lot of problems concerning how to solve this kind of questions and how to deal with them. Most of the time we don't have enough time when we are solving the AP calculus a b or BC questions, and we need to have a lot of tools to deal with this kind of questions. That's why here. This is the best place and this is the best way to learn about. Solving problems concerning AP calculus a b and BC. If when I prepare for the Berkeley math competition Or the Stanford math competition, this is the best place where you can learn a lot of techniques that you can use to participate. We also going to use mit Be integration And we're gonna have a lot of questions.