Mathematics

Problem

Consider the following expression involving an acute angle

\theta

E(\theta)=\frac{\sec^{2}\theta-\tan^{2}\theta}{\csc^{2}\theta-\cot^{2}\theta}

Answer the questions that follow. a. (i) State any two reciprocal trigonometric identities. b. (ii) Simplify

E(\theta)

and show that it reduces to a numerical constant independent of

\theta

. c. (iii) Verify the value obtained in part (ii) for

\theta=30^{\circ}

, showing each step clearly.