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

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

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

Prove the following: (frac(cos2theta)(1+sin2theta))=tan(pi/4-0)

Prove the following: cottheta(1-cos2theta)=sin2theta

Prove the following: (frac(1-cos2theta+sin2theta)(1+cos2theta+sin2theta))=tantheta

Prove the following: tan^-1(sqrt(frac{1-costheta}{1+costheta})) = frac{theta}{2} , if theta lies in (-pi,pi)

Prove the following: (frac(sin^3theta+cos^3theta)(sintheta+costheta))+(frac(sin^3theta-cos^3theta)(sintheta-costheta))=2

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

Prove the following: frac(tan(theta/2)+cot(theta/2))(cot(theta/2)-tan(theta/2))=sectheta

Prove the following: cos^4theta-sin^4theta+1=2cos^2theta