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

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

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

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

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

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

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

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

Prove that (sin theta- "cosec" theta )(cos theta- sec theta )=(1)/(tan theta + cot theta).

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

Prove that: sin4 theta=4 sin theta cos^(3)theta-4cos theta sin^(3)theta