Simplify the following expression and find all solutions ove

Simplify the following expression and find all solutions over the interval [0, 2pi): cos(x + pi/6)+ cos (x - pi/6) = sin(2x)

cos(A + B) = cos A cos B sin A sin B

cos(A B) = cos A cos B + sin A sin B

Now cos(x + 30) + cos(x - 30) = sin(2x)

cos x cos30 sin x sin30 + cos x cos30 + sin x sin30 = sin2x

2*cos x cos30 = 2*sinx*cos x

sin x = cos 30 = 0.866

x = 60

In given region, x = 60, 120