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

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

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

Prove the following: (frac(sintheta)(1+costheta))=tan(theta/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 identities: (frac(tan^3theta)(1+tan^2theta))+(frac(cot^3theta)(1+cot^2theta))=secthetacosectheta-2sinthetacostheta

Prove the following : ( sec theta + tan theta ) ( 1-sin theta ) = cos theta

tantheta . Cot theta =

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

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