Prove $\sin^4\theta+\cos^4 \theta= 1-2\sin^2 \theta cos^2 \theta $ Is it possible to prove:
$$\sin^4\theta+\cos^4 \theta= 1-2\sin^2 \theta cos^2 \theta ?$$

Observe that
\begin{align*}
\sin^4\theta+\cos^4\theta=1-2\sin^2\theta\cos^2\theta
&\Longleftrightarrow \sin^4\theta+\cos^4\theta+2\sin^2\theta\cos^2\theta=1\\
\end{align*}
which is always true since
$$
\sin^4\theta+\cos^4\theta+2\sin^2\theta\cos^2\theta=(\sin^2\theta+\cos^2\theta)^2=1^2=1
$$
so the identity is proved.
