`(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))

If ((1+sin theta-cos theta))/((1+sin theta+cos theta))+((1+sin theta+cos theta))/((1+sin theta-cos theta))=4 , then which of the following values will be suitable for theta ? यदि ((1+sin theta-cos theta))/((1+sin theta+cos theta))+((1+sin theta+cos theta))/((1+sin theta-cos theta))=4 है, तो theta के लिए निम्नलिखित में से कौन सा मान उपयुक्त होगा?

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

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

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

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

(1+sin2 theta-cos2 theta)/(1+sin2 theta+cos2 theta)=tan theta

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

The value of ((sin theta -cos theta )(1+tan theta + cot theta ))/(1+sin theta cos theta ) = ?