Question

Simplify: (sin Θ − cos Θ)2 + (sin Θ + cos Θ)2

Answer 1

The answer is simply the number 2! Nice ...

s= sin(angle), c=cos(angle) -do this in general and save some writing!

(s+c)^2 +(s-c)^2 = s^2 + 2sc+c^2 + s^2 -2sc+c^2 = 2*(s^2+c^2) =2*1=2!