[Math] How to simplify $(\sin\theta-\cos\theta)^2+(\sin\theta+\cos\theta)^2$

Question

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.

Answer 1

Hint:

1) Expand : $(a+b)^2$ and $(a-b)^2$ for all real numbers $a$ and $b$.

2) What is the value of $\sin^2(x) + \cos^2(x)$ for all real number $x$ ?