Question

Find all values of x in the interval [0, 2π] that satisfy the equation.
3 sin(2x) = 3 cos(x)

Answer 1

3 sin ( 2 x ) = 3 cos x
3 · 2 sin x cos x - 3 cos x = 0
6 sin x cos x - 3 cos x = 0 /: 3
2 sin x cos x - cos x = 0
cos x ( 2 sin x - 1 )
cos x = 0,
x 1 = π/2, x 2 = 3π/2;
2 sin x - 1 = 0
2 sin x = 1
sin x = 1/2
x 3 = π/6, x 4 = 5π/6.