Prove `sin^2 theta + cos^2 theta=1`

Prove:- sin^2 theta / cos theta+ cos theta += 1/cos theta

prove that sin^2theta+cos^2theta=1

Prove the identity sin^(2)theta + cos^(2) theta = 1 with the help of given figure .

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

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

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

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

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

Given that sin theta+2cos theta=1 then prove that 2sin theta-cos theta=2