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

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

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

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

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

Prove the following: tan(pi/4-theta)=(frac(1-tantheta)(1+tantheta))

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

Prove the following: tan2theta+sec2theta=(frac(1+tantheta)(1-tantheta))

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

Prove the following ((1+cottheta+tantheta)(sintheta-costheta))/(sec^3theta-cosec^3theta)=sin^2thetacos^2theta

Solve the following:Prove that (frac(cos^3theta-cos3theta)(costheta))+(frac(sin^3theta+sin3theta)(sintheta))=3