Prove that `(frac(1-tantheta)(1-cottheta))^2=tan^2 theta`

Prove that (1+tantheta)^(2)+(1+cottheta)^(2)=(sectheta+"cosec "theta)^(2) .

Prove that (frac(1+sintheta)(1+costheta)) + (frac(1-sintheta)(1-costheta)) = 2(cosec^2theta-cottheta)

Prove the following: (frac(sintheta)(1+costheta))=tan(theta/2)

Prove the following: (frac(1-cos2theta)(1+cos2theta))=tan^2theta

Prove the following: sqrt(frac(1-cos2theta)(1+cos2theta))=tantheta

Prove the following: (frac(tantheta+sectheta-1)(tantheta+sectheta+1))=(frac(tantheta)(sectheta+1))

prove that (tan theta) / (sec theta -1) = (tan theta + sec theta + 1) / (tan theta + sec theta - 1)

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

Prove the following: ((tantheta+(1)/(costheta))^2+((tantheta-(1)/(costheta))^2=2(frac(1+sin^2theta)(1-sin^2theta))

Prove that (frac(sintheta-2sin^3theta)(2cos^3theta-costheta))=tantheta