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

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

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

3. sin^(3)theta+cos^(3)theta=(sin theta+cos theta)(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?

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

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

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

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