Question

sin thita + sin 2 thita + sin 4 thita + sin 5 thita ÷ cost thita + cos 2 thita + cos 4 thita + cos 5 thita​

Answer 1

$\frac{ ( \sin(2 \theta) + \sin(4 \theta)) + ( \sin(\theta) + \sin(5\theta) ) }{( \cos(2\theta) + \cos(4\theta) ) + ( \cos(\theta) + \cos(5\theta) )}$

$= \frac{2 \sin(3 \theta) \cos( \theta) + 2 \sin(3\theta) \cos(2\theta) }{2 \cos(3 \theta) \cos( \theta) + 2 \cos(3 \theta) \cos(2 \theta) }$

$= \tan(3\theta )$