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

Prove that: (i) sec^(4)A-sec^(2)A="tan"^(4)A+"tan"^(2)A (ii) "sin"^(8)theta-cos^(8)theta=("sin"^(2)theta-cos^(2)theta)(1-2"sin"^(2)thetacos^(2)theta) .

prove that- sin^2theta/cos^2theta+cos^2theta/sin^2theta=1/ (sin^2thetacos^2theta)-2

Prove that (sin^(4)theta-cos^(4)theta)/(sin^(2)theta-cos^(2)theta)=1

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

Prove that : (1+sin2 theta-cos 2theta)/(sin theta+cos theta)=2sin theta

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

Prove that sin^(6)theta+cos^(6)theta=1-3sin^(2)theta.cos^(2)theta.

Find the value of (sin^4theta+cos^4theta)/(1-2sin^2 thetacos ^2 theta)