Prove that `(2 sin theta - sin 2theta)/(2 sin theta + sin 2theta) = tan^2\ theta/2`

Prove that : (1+ sin theta - cos theta) / (1+ sin theta + cos theta ) = tan (theta/2)

(sin theta + sin 2 theta)/( 1 + cos theta + cos 2 theta) = tan theta.

Prove that (1- cos theta + sin theta)/( 1+cos theta +sin theta) = "tan"(theta)/(2) .

Prove that (cos theta+sin theta )^2 + (cos theta - sin theta )^2 =2

sin^(3)theta + sin theta - sin theta cos^(2)theta =

(1+sin 2theta+cos 2theta)/(1+sin2 theta-cos 2 theta) =

Prove that: sin theta- 1/2 sin 2 theta+1/3 sin 3theta-…to oo = theta/2

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

Prove that : (sin theta + 2 sin 3theta + sin 5theta)/(sin 3theta + 2 sin 5theta + sin 7theta) = (sin 3theta)/(sin 5theta)

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