Solve the given equation over the interval [0, 2π): 2 cos x − sin2 x = cos2 x.

Question

Solve the given equation over the interval [0, 2π): 2 cos x − sin2 x = cos2 x.

 

A. x=(5pi/6) and x=(7pi/6)

B. x=(2pi/3) and x=(4pi/3)

C. x=(pi/6) and x=(11pi/6)

D. x=(pi/3) and x=(5pi/3)

Solve the given equation over the interval [0, 2π): 2 cos x − sin2 x = cos2 x.

Answer 1

2 cos x - sin² x = cos² x

2 cos x = sin² x + cos² x       Pythagorean identity

2 cos x = 1

 

Can you solve for x?