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

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

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

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

If sin theta+cos theta=1 then sin theta cos theta=

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

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

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