Prove the following identities:
`(sin theta-cos theta+1)/(sin theta+cos theta-1)=(1+sin theta)/(cos 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 the following identities: (sin^(3)theta+cos^(3)theta)/(sin theta+cos theta)+sin theta cos theta=1

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 identity : (sin theta)/(1+cos theta)+ (sin theta)/(1-cos theta)= 2/(sin theta) .

(sin theta+cos theta)(1-sin theta cos theta)=sin^3 theta+cos^3 theta

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

Prove the following identity : sin theta cot theta+ sin theta cosec theta=1 + cos theta .

cos theta/(1+sin theta)=(1-sin theta)/cos theta

Prove the following : (sin theta -cos theta + 1)/(sin theta + cos theta - 1) = (1)/ (sec theta - tan theta)

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