Prove that `1-cos^2theta-sin^2theta=0`

Prove that cos^2theta=1-sin^2theta

Prove that cos^6 theta-sin^6theta=cos2theta(1-1/4 sin^2 2 theta)

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

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

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

If sin theta+sin^(2)theta=1 Prove that cos^(2)theta+cos^(4)theta=1

Prove that (1+cos theta)/(sin theta)=cot[(theta)/(2)]

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

Prove that : (1-cos theta+i sin theta)/(1+i sin theta+cos theta)=ie^(-1)tan((theta)/(2))

If sin theta+sin^(2)theta=1, prove that cos^(2)theta+cos^(4)theta=1