Prove that : `(sin theta + sin 3theta + sin 5theta)/(cos theta + cos 3theta + cos 5theta) = tan 3theta`

Prove that (sin theta + sin 3theta+ sin 5 theta + sin 7theta)/(cos theta + cos 3theta + cos 5 theta + cos 7theta) = (tan 3theta + tan theta)/(1 - tan 3theta tan theta) .

(sin5 theta-2sin3 theta + sin theta) / (cos5 theta-cos theta) = tan theta

(sin theta+sin3 theta+sin5 theta)/(cos theta+cos3 theta+cos5 theta)=tan3 theta

Prove that :(sin5 theta-2sin3 theta+sin theta)/(cos5 theta-cos theta)=tan theta

(sin 3theta)/(sin theta)-(cos 3theta)/(cos theta)=

(sin 3 theta + sin 5 theta + sin 7 theta + sin 9theta)/(cos 3 theta + cos 5 theta + cos 7 theta + cos 9 theta )=

Prove that (sin theta - 2 sin^(3) theta)/(2 cos^(3) theta - cos theta) = tan theta

Prove that (tan 5theta + tan 3theta)/(tan 5theta - tan 3theta) = 4 cos 2theta cos 4theta

2 cos (theta - pi //2) + 3 sin (theta + pi//2) - (3sin theta + 2 cos theta ) = ? A. cos theta - sin theta B. sin theta - cos theta C. sin theta + cos theta D. cot theta - tan theta .

Prove that : sin theta/cos(3theta) +sin (3theta)/cos (9theta) + sin(9theta)/cos( 27theta )= 1/2(tan27 theta -tan theta)