Mathematics

Problem

(i) State the fundamental trigonometric identity that relates

\sin^2\theta

and

\cos^2\theta

for any acute angle

\theta

. (ii) Starting from the identity stated in part (i), obtain the relation

\sin^2\theta = (1-\cos\theta)(1+\cos\theta)

. (iii) Hence or otherwise, simplify the expression

\dfrac{\sin^2\theta}{1-\cos\theta}

and show that it equals

1+\cos\theta

for every acute angle

\theta