Question

Find the general solution
sin^2 2theta=1-cos2theta

Answer 1

\[\sin^2 2\theta=1-\cos2\theta\]

Answer 2

\[\sin^2 2 \psi = 1- \cos 2 \psi \implies 1-\cos^2 2 \psi = 1-\cos 2 \psi \implies \cos^2 2 \psi - \cos 2 \psi \]
\[= 0 \implies \cos2 \psi(\cos2 \psi - 1)=0 \implies \cos2 \psi = 0; \cos2 \psi = 1 \]
\[\implies \psi = \frac{(2n+1) \pi}{4}; \psi = 2n \pi; n \in \mathbb{Z} \]