<s>[INST] Prove $\sin^4\theta+\cos^4 \theta= 1-2\sin^2 \theta cos^2 \theta $ Is it possible to prove:
$$\sin^4\theta+\cos^4 \theta= 1-2\sin^2 \theta cos^2 \theta ?$$
 [/INST] Another direct way would be to use $\cos^2\theta+\sin^2 \theta=1$ also in the forms $\sin^2 \theta = 1-\cos^2 \theta$ and $\cos^2 \theta = 1-\sin^2 \theta$ as follows:
$$\sin^4 \theta + \cos^4 \theta = \sin^2 \theta (1-\cos^2\theta)+\cos^2 \theta(1-\sin^2\theta)=1-2\sin^2\theta\cos^2\theta$$
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