-sin^2x=2cosx-2

Answer 1

- sin²x = 2 cosx - 2

Use Pythagorean theorem  sin²x = 1- cos²x

- (1- cos²x)= 2 cosx - 2

-1 + cos²x = 2 cosx - 2

cos²x - 2 cosx +1 =0

Use formula a² - 2ab + b² = (a - b)²

(cosx - 1)² =0

cosx =1

cos x = cos 0

The general solution for cos x = cos 0 is x = 2nπ ± 0

The solution is x = 2nπ