Show :
`Sin^(2)theta=1-cos^(2)theta`

Show : 1 - Sin^4theta = Cos^2theta ( 1 + Sin^2theta )

Show that (cos^(2)theta - sin^(2)theta)=(2tan theta)/((1- tan^(2)theta)) is not an identity .

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

Prove the following 1.((1-cos^(2)theta)/(sin^(2)theta))=12.1-((cos^(2)theta)/(1+sin theta))=sin theta

Show : Sin^4theta - Cos^4theta = Sin^2theta - Cos^2theta

(2sin theta*cos theta-cos theta)/(1-sin theta+sin^(2)theta-cos^(2)theta)=cot theta

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

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