If $\cos\theta = \sin\theta$, then what is $\cos2\theta$?
I am stuck on this problem, please help.
The tips made above are perfectly reasonable but let me provide an algebraic answer.
Using the addition formula $\cos(x+y) = \cos(x) \cos(y) - \sin(x) \sin(y)$, we know that $\cos(2x) = \cos(x+x) = \cos(x) \cos(x) - \sin(x) \sin(x)$
Does that help you now?
We have $\cos\theta=\sin\theta$ if $\theta=\pi/4+2k\pi$ or $\theta=3\pi/4+2k\pi$. In both of these situations, $\cos 2\theta=0$.