Evaluate :

`Cos^2( 2theta ) + Sin^2( 2theta )`

Evaluate : ( Cos^2theta - Sin^2theta ) / ( ( Costheta - Sintheta )^2

Evaluate : ( Cos^2theta - Sin^2theta ) / ( ( Costheta - Sintheta )^2

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

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

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

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))

Find the maximum and minimum value of cos^(2) theta- 6 sin theta cos theta + 3 sin^(2) theta + 2 .

If sin^(2) theta +2 cos^(2) theta + 3 sin^(2) theta + 4 cos^(2) theta+….+ 40 term =405 where theta is acute, then find the value of tan theta .