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

(sin theta-cos theta)^(2)*(sin theta+cos theta)^(2)=

((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))

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

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

If a^(2) =(1+2 sin theta cos theta)/(1-2sin theta cos theta) , then what is (a+1)/(a-1) equal to?

The value of (cos^6 theta+sin^6 theta+ 3sin^2 theta cos^2 theta)/(cosec theta sec theta(sin theta+cos theta-1)(sin theta+cos theta+1)) is : (cos^6 theta+sin^6 theta+ 3sin^2 theta cos^2 theta)/(cosec theta sec theta(sin theta+cos theta-1)(sin theta+cos theta+1)) का मान ज्ञात कीजिए?

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