`(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?

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 ।

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?