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.

Since this is a multiple-choice question, you can very quickly narrow down the answer by plugging in values of $\theta$. For example, when $\theta = 0$, the expression becomes $(0-1)^2+(0+1)^2 = 2$.
Now, looking at the four options and evaluating at $\theta = 0$, we have:


*

*$1$

*$2$

*$\sin^2 \theta = 0^2 = 0$

*$\cos^2 \theta = 1^2 = 1$


The answer is clearly the second option.
