How do you solve 2 sin squared x plus sin x equals 1?

Answer 1

2 sin2 x + sin x = 1.

Letting s = sin x, we have:

2s2 + s - 1 = (2s - 1)(s + 1) = 0; whence,

sin x = ½ or -1, and

x = 30° or 150° or 270°.

Or, if you prefer,

x = π/6 or 5π/6 or 3π/2.