Solve trigonometric equation $ 3 \cos x + 2\sin x=1 $ Solve trigonometric equation: $$ 3 \cos x + 2\sin x=1 $$
I tried to substitue $\cos x = \dfrac{1-t^2}{1+t^2}, \sin x = \dfrac{2t}{1+t^2}$. Yet with no results.

If you have a sum $S=a\cos x+b \sin x$ 
define $r$ by $r^2=a^2+b^2$ 
and $\theta$ by $r\sin \theta =a$ and $r\cos \theta =b$ so that $\tan \theta =\cfrac ab$
Then $S=r\sin \theta \cos x+r\cos \theta \sin x=r\sin (x+\theta)$
