solve for x: sin x/2 + cos x = 0

Answer 1

The easiest way would be to let y =x/2

Then, sin y + cos 2y = 0

sin y + 1 - 2 sin²y= 0

2sin²y -sin y - 1 = 0

(2sin y + 1)(sin y - 1) = 0

sin y = -1/2, 1

y = 90°, 210°, 330°

Then, x = 2y = 180°, 420°, 660°