 Hello and welcome to the session. Let us understand the following problem today. Solve the following equation 2 tan inverse cos x is equal to tan inverse of 2 cos x. Let us write the property we will be using. 2 tan inverse x is equal to tan inverse 2x by 1 minus x square. This is the key idea that we will be using in our problem. Now let us write the solution. We have to solve the equation that is 2 tan inverse of cos x is equal to tan inverse of 2 cos x. Consider LHS that is 2 tan inverse of cos x which is equal to tan inverse of 2 cos x by 1 minus cos square x using the formula in key idea. Now LHS which is equal to tan inverse of 2 cos x. Now which implies putting LHS equal to RHS it implies tan inverse 2 cos x by 1 minus cos square x is equal to tan inverse of 2 cos x. Which implies 2 cos x by 1 minus cos square x is equal to 2 cos x. Which implies cos x this cancels so we will if cos x by 1 minus cos square x is equal to 1 by sin x. Which implies cos x by sin square x is equal to 1 by sin x. Which implies cos x is equal to sin x which implies tan x is equal to 1 which implies x is equal to pi by 4. Therefore the required answer is x is equal to pi by 4.