Question

Will give medal!
Simplify:(sin Θ − cos Θ)^2 + (sin Θ + cos Θ)^2

Answer 1

Well, if you were to foil out each of those two groups, you would have:
\[\sin^{2}\theta -2\sin \theta \cos \theta+ \cos^{2}\theta + \sin^{2}\theta + 2\sin \theta \cos \theta +\cos^{2} \theta\]
Doing this, we can see that we have two terms that would cancel. Combining like terms for whats remaining, we would have:
\[2\sin^{2}\theta + 2\cos^{2}\theta = 2(\sin^{2} \theta + \cos^{2} \theta)\]
So with whats remaining, do you see anything you can do further to get a finite answer? :)

Answer 2

Could we cancel out the sin and cos to be left with 2? @Concentrationalizing

Answer 3

Yep, absolutely. Because we have the identity sin^2(x) + cos^2(x) = 1, so we would be left with 2(1) = 2

Answer 4

Thank you so much !

Answer 5

No problem :)