Prove and confirm a numerical result for the given trigonometric expression.

MATHEMATICS · Multi-part · CBSE · Mathematics · Introduction to Trigonometry · Introduction to Trigonometry

Problem

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

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

for every angle

\theta

. (ii) Evaluate both squares separately for

\theta=30^{\circ}

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