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

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

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

Prove the following: tan^2theta-sin^2theta=Sin^4thetasec^2theta

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

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

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

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

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

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

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