TITLE: Solve $\cos2A+\sin A=2$
QUESTION [5 upvotes]: So they tell me solve $\cos2A+\sin A=2$.
Ok guys I found the problem :/ I was wondering why he gave us this question but its actually 
$$\cos2A+\sin A=-2$$
and I simplified to 
$-2x^2+x+3=0$, which has solutions $x= 3/2$, $x=-1$
So I'm guessing then I go but this cannot be found so once again I am lost.

REPLY [9 votes]: Since $\cos 2 A \leq 1$ and $\sin A \leq 1$, you must have equality in both. Equation in sine gives $A = {\pi \over 2} + 2 k \pi$, and then $\cos 2 A = \cos \pi = -1$, contradiction. There is thus no solution.