Mathematics

Problem

Consider the expression

E = \frac{\sin^{2}\theta}{\cos^{2}\theta}+\frac{\cos^{2}\theta}{\sin^{2}\theta},

where

\theta

is an acute angle. (i) State the fundamental trigonometric identity that relates

\sin^{2}\theta

and

\cos^{2}\theta

. (ii) Rewrite each fraction in

E

so that the identity stated in part (i) can be applied. (iii) Simplify

E

completely and state its final value.