Question

How do you solve `sin2x = cosx` from [-2pi, pi/2]#?

Answer 1

Solve sin 2x = cos x

Explanation:

sin 2x - cos x = 0
2sin x.cos x - cos x = 0
cos x(2sin x - 1) = 0

a. cos x = 0 -->`x = pi/2` and `x = (3pi)/2`

b. `sin x = 1/2` --> `x = pi/6` and `x = pi - pi/6 = (5pi)/6`

Answers: `pi/6, pi/2, (5pi)/6, (3pi)/2`