Evaluate :

`1/( Sin^2( theta ) - Cos^2( theta ) )`

Evaluate : Sin^6theta + Cos^6theta = 1 - k Sin^2theta Cos^2theta , find k

Evaluate int((2 sin theta + sin 2 theta)d theta)/((cos theta-1)sqrt(cos theta + cos^(2) theta + cos^(3) theta)) .

If cos theta>sin theta>0, then evaluate : int{log((1+sin2 theta)/(1-sin2 theta))^(cos^(2)theta)+log((cos2 theta)/(1+sin2 theta))}d theta

If sin theta=12/13 find the value of (sin^2 theta-cos^2 theta)/(2sin theta cos theta)xx1/(tan^2 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))

Evaluate sin^2theta/cos^2theta+1

Evaluate: int cos2 theta ln((cos theta+sin theta)/(cos theta-sin theta))d theta

If sin theta=(12)/(13), find the value of (sin^(2)theta-cos^(2)theta)/(2sin theta cos theta)xx(1)/(tan^(2)theta)

If cos theta=(5)/(13), find the value of (sin^(2)theta-cos^(2)theta)/(2sin theta cos theta)xx(1)/(tan^(2)theta)