I was asked to find a formula for $\cos(5x)$ in terms of $\sin(x)$ and $\cos(x)$.
I tried to use the formula $\cos(5x) + i\sin(5x) = (\cos(x)+i\sin(x))^5 $ and what I get is $16i\sin^5(x) - 20i\sin^3(x) + 5i\sin(x) + \cos(x) + 16 \sin^4(x) \cos(x) - 12 \sin^2(x) \cos(x)$
But how do I deal with the $i\sin(5x)$? Because I only can use $\sin(x)$ and $\cos(x)$ to express $\cos(5x)$. Thank you for your help!