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

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

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

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

Prove the following identities: 2(sin^6theta+cos^6theta)-3(sin^4theta+cos^4theta)+1=0 sin^6theta+cos^6theta+3sin^2thetacos^2theta=1 (sin^8theta-cos^8theta)=(sin^2theta-cos^2theta)(1-2s in^2thetacos^2theta)

Prove that : sin^8 theta- cos^8 theta= (sin^2 theta- cos^2 theta)(1-2 sin^2 theta cos^2 theta) .

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

prove : sin^8θ-cos^8θ = (sin^2 theta - cos^2 theta) (1- 2 sin^2 theta cos^2 theta)

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