Prove the following identity: `(1/(sec^2theta-cos^2theta)+1/(cos e c^2theta-sin^2theta))sin^2thetacos^2theta=(1-sin^2thetacos^2theta)/(2+sin^2thetacos^2theta)`

Prove that (1/(sec^2theta-cos^2theta)+1/(cosec^2-sin^2theta))sin^2thetacos^2theta=(1-sin^2thetacos^2theta)/(2+sin^2thetacos^2theta

sin^4theta+2sin^2thetacos^2theta=1-cos^4 theta

Prove the following identity: ((1)/(sec^(2)theta-cos^(2)theta)+(1)/(cos ec^(2)theta-sin^(2)theta))sin^(2)theta cos^(2)theta=(1-sin^(2)theta cos^(2)theta)/(2+sin^(2)cos^(2)theta)

Prove: tan^2thetacos^2theta=1-cos^2theta

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

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

Prove that sin^4theta+cos^4theta=1-2sin^2thetacos^2theta .

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

sin^(6)theta+cos^(6)theta=1-3sin^(2)thetacos^(2)theta

sin^(6)theta=cos^(6)theta=1-3sin^(2)thetacos^(2)theta