Question

Find all solutions to the equation.

Answer 1

If the equation is

$7\sin^2x-14\sin x+2=-5$

then rewrite the equation as

$7\sin^2x-14\sin x+7=0$

Divide boths sides by 7:

$\sin^2x-2\sin x+1=0$

Since $x^2-2x+1=(x-1)^2$, we can factorize this as

$(\sin x-1)^2=0$

Now solve for x :

$\sin x-1=0$

$\sin x=1$

$\implies\boxed{x=\dfrac\pi2+2n\pi}$

where n is any integer.

If you meant sin(2x) instead, I'm not sure there's a simple way to get a solution...