`sin^2 theta /(cos theta +1) - sin^2 theta /(cos theta-1)` =?

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

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

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

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

cos theta sqrt(1-sin^(2)theta)=

int (d theta)/((sin theta - 2 cos theta)(2 sin theta + cos theta))

(2 sin theta*cos theta - cos theta)/(1-sin theta+sin^2 theta-cos^2 theta) = cot theta

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

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