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

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

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

Prove that ((1+cottheta+tantheta)(sintheta-costheta))=(frac(sectheta)(cosec^2theta))-(frac(cosectheta)(sec^2theta))

Prove the following: sin^8theta-cos^8theta=(sin^2theta-cos^2theta)(1-2sin^2thetacos^2theta)

Prove that sin^6theta+cos^6theta=1-3sin^2thetacos^2theta

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

Prove the following : cot^2 theta - tan^2 theta = cosec^2 theta -sec^2 theta

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

Prove the following : tan^4 theta + tan^2 theta = sec^4 theta -sec^2 theta

Prove that (frac(sintheta-2sin^3theta)(2cos^3theta-costheta))=tantheta