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

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

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

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

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

Prove that sin theta cos^(3)theta - cos theta sin^(3) theta = (1)/(4) sin 4 theta .

Prove that (sin theta - 2 sin^(3) theta)/(2 cos^(3) theta - cos theta) = tan theta

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

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

Prove that : sin theta/cos(3theta) +sin (3theta)/cos (9theta) + sin(9theta)/cos( 27theta )= 1/2(tan27 theta -tan theta)

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