<s>[INST] Simple trigonometry equation The previous class we were doing trigonometry exercises. Before the class finished, our teacher wrote exercises on the table. I am stuck with the following one:
$$
\cos(2x) + 1 + 3\sin x = 0
$$
I have come up with this:  
$$
1= \sin^2 x + \cos^2 x
$$
$$
\cos(2x) = \cos^2 x - \sin^2 x
$$
When we substitute we get
$$
2\cos^2 x + 3\sin x = 0
$$
Need to find $x\ldots$
 [/INST] $$\cos(2x)+1+3\sin x=0$$
now let's substitute $\cos (2x)=1-2\sin^2x$
$2-2\sin^2x+3\sin x=0$
And then, if we denote $y=\sin x$ we get a quadratic equation
$$2-2y^2+3y=0$$
</s>