How to simplify $(\sin\theta-\cos\theta)^2+(\sin\theta+\cos\theta)^2$? Simplify: $(\sin \theta − \cos \theta)^2 + (\sin \theta + \cos \theta)^2$
Answer choices:


*

*1

*2

*$ \sin^2 \theta$

*$ \cos^2 \theta$


I am lost on how to do this. Help would be much appreciated.

$$\begin{align}
&\phantom{=}\left(\sin x-\cos x\right)^2+\left(\sin x+\cos x\right)^2\\
&=\sin^2x-2\sin x\cos x+\cos^2x+\sin^2x+2\sin x\cos x+\cos^2x\\
&=2\sin^2x+2\cos^2x\\
&=2\left(\sin^2x+\cos^2x\right)\\
&=2
\end{align}$$
