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

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

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

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

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

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

Prove the following: sqrt(frac(1+sin2x)(1-sin2x))=tan(pi/4+x)

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

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

Prove the following: tan^-1(frac{costheta+sintheta}{costheta-sintheta}) =frac {pi}{4}+theta if theta belongs to (-frac{pi}{4},frac{pi}{4})

Select and write the correct answer from the given alternatives in each of the following: (frac(1+2sin^2theta)(1+3tan^2theta)) =…….