Mathematics

Problem

The expression

\dfrac{\sin 3\theta+\sin\theta}{\cos 3\theta+\cos\theta}

is to be simplified. a. (i) Show that the expression simplifies to

\tan 2\theta

for all values of

\theta

for which it is defined. b. (ii) Using the result of part (i), calculate the numerical value of

\dfrac{\sin75^{\circ}+\sin25^{\circ}}{\cos75^{\circ}+\cos25^{\circ}}.