How to Solve a Trig Equation for x with Cosine and Sine Terms

[Wessssss]

Homework Statement

cos^2x+2sin^2x=-1

Solve for x

Homework Equations

The Attempt at a Solution

I don't really know how to start. I know cos^2x+sin^2x=1 but I don't think I can apply that with the 2 thrown in there.

 

[SteamKing]

Observe: cos^2 + 2 sin^2 = (cos^2 + sin^2) + sin^2

 

[Wessssss]

thank you

 

[HallsofIvy]

Or, if it weren't quite that obvious, you could have replaced $cos^2(x)$ with $1- sin^2(x)$. That is, $cos^2(x)+ 2sin^2(x)= (1- sin^2(x))+ 2sin^2(x)= 1+ sin^2(x)= 1.$