Mathematics

Problem

Prove and confirm a numerical result for the given trigonometric expression. a. (i) Show that

(\sin\theta-\cos\theta)^{2}+(\sin\theta+\cos\theta)^{2}=2

for every angle

\theta

. b. (ii) Evaluate both squares separately for

\theta=30^{\circ}

and add the results to confirm the equality obtained in part (i).