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

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

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

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

Prove that : 2 sin^2 theta + 4 cos (theta + alpha) sin alpha sin theta + cos 2 (alpha + theta) is independent of theta.

If 2 cos theta = sqrt3. prove that : 3 sin theta - 4 sin ^(3) theta =1

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

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

Prove that 1-cos^(2)theta-sin^(2)theta=0

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

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