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(cos2theta)(1+sin2theta))=tan(pi/4-0)

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

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 identities: (frac(sintheta)(1+costheta))+(frac(1+costheta)(sintheta))=2cosectheta

Prove the following: (sintheta+cosectheta)^2+(costheta+sectheta)^2=Tan^2theta+cot^2theta+7

Prove the following: (frac(cosectheta+cottheta-1)(cosectheta+cottheta+1))=(frac(1-sintheta)(costheta))

Select and write the correct answer from the given alternatives in each of the following: (frac(3costheta+cos3theta)(3sintheta-sin3theta)) =