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

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))

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

Simplify: (sin8 theta cos theta-sin6 theta cos3 theta)/(cos2 theta cos theta-sin3 theta sin4 theta)

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

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

cos theta+sin theta=cos2 theta+sin2 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)/(sin theta-cos theta)=3 and theta is an acute angle, then the value of (3sin theta+4cos theta)/(8cos theta-3sin theta) is: यदि (sin theta+cos theta)/(sin theta-cos theta)=3 तो (3sin theta+4cos theta)/(8cos theta-3sin theta) का मान ज्ञात करें ।

If (sin theta+cos theta)/(sin theta-cos theta)=3 then sin^4 theta-cos^4 theta=