# Thread: Trigonometric identity

1. ## Trigonometric identity

How I solve the equation:
sin2x + sinx = 2

?

2. ## Re: Trigonometric identity

let $u = \sin(x)$

solve the resulting quadratic.

ensure the values obtained are valid and discard the invalid ones

solve for $x$ via $x = \arcsin(u)$

note that $\sin(x)$ is periodic and adjust the solution accordingly