Solve for x, trigonometric function

Question

Solve for x. 3cos^2x + cosx = sin^2x

But do not use Accos

Answer 1

Study the Pythagorean Identities

3 cos² x + cos x = 1 - cos² x

4 cos² x + cos x - 1 = 0

Let u = cos x

4 u² + u - 1 = 0

u = (-1 ±√17) / 8

x = acrcos (-1 ±√17) / 8