Mathematics

Problem

Let

\sin\theta=\dfrac{3}{5}

where

0<\theta<\dfrac{\pi}{2}

. a. (i) Find

\cos\theta

and

\tan\theta

. b. (ii) Calculate the exact values of

\sin3\theta

\cos3\theta

and

\tan3\theta

. c. (iii) Hence evaluate

\sin3\theta+\cos3\theta

and state its value.