Simplify a higher-power trigonometric expression and apply it to a specific angle.

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

Problem

Simplify a higher-power trigonometric expression and apply it to a specific angle. (i) Prove that

\sin^{4}\theta+\cos^{4}\theta=1-2\sin^{2}\theta\cos^{2}\theta

for any acute angle

\theta

. (ii) Using

\theta=60^{\circ}

, determine the numerical value of

\sin^{4}\theta+\cos^{4}\theta