How to solve $\cos^{40}x-\sin^{40}x=1$ for real and imaginary solutions Solve : $$\cos^{40}x-\sin^{40}x=1$$
I found by induction that $\sin(x)=0$ satisfy the equation so $$x=n\pi$$ must be the solution but there should be more solutions real or imaginary , how to find them ?

HINT
I would recommend you to notice that
\begin{align*}
\cos^{40}(x) - \sin^{40}(x) = 1 & \Longleftrightarrow \cos^{40}(x) = \sin^{40}(x) + 1 \geq 1
\end{align*}
Based on such relation, can you proceed from here?
