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

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

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

Prove that (cos^3 theta-sin^3 theta)/(cos theta-sin theta) = 1+cos theta sin theta

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

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

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

Prove that cos^6 theta+ sin^6 theta= 1-3sin^2 theta cos^2 theta