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

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

Prove that : (cos 4theta + cos 3theta + cos 2theta)/(sin 4theta + sin 3theta + sin 2theta) = cot 3theta

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

Prove that : (sin 5theta + sin 3theta)/(cos 5theta + cos 3theta) = tan 4theta

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

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

Prove that ( cos theta + cos 2 theta + cos 3 theta + cos 4 theta)/(sin theta + sin 2 theta + sin 3 theta + sin 4 theta)= cot ""(5theta)/(2).

Prove that : sin theta cos^3 theta - cos theta sin^3 theta = 1/4 sin4theta .

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