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

Prove that : (sintheta-costheta)/(sintheta+costheta)+(sintheta+costheta)/(sintheta-costheta)=(2)/(2sin^(2)theta-1)

Prove that sin^(3)theta+cos^(3)theta=(sintheta+costheta)(1-sin thetacostheta) .

Prove that: (1+sintheta-costheta)/(1+sintheta+costheta)=tan(theta/2)

Prove that: 3(sintheta-costheta)^4+6(sintheta+costheta)^2+4(sin^6theta+cos^6theta)-13=0.

Prove that : (sintheta +sin2theta)/(1+costheta+cos2theta)=tantheta

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

Prove that: (sin2theta)/(costheta cos3theta)+(sin4theta)/(cos3theta.cos5theta)+(sin6theta)/(cos5theta.cos7theta)+… to terms = 1/(2sintheta) [sec(2n+1)theta-sectheta]

Prove that (1+costheta-sin^(2)theta)/(sintheta(1+costheta))=cottheta

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

Prove that : (sintheta-2sin^(3)theta)/(2cos^(3)theta-costheta)-tantheta