Find `(1-cos^2 theta)/ sin^2theta` =?

Prove that (1 - cos 2 theta)/( sin 2 theta) = tan theta.

If cottheta=1/(sqrt(3)) , find the value of (1-cos^2theta)/(2-sin^2theta)

cos theta sqrt(1-sin^(2)theta)=

If "cosec" theta = sqrt5 , find the value of : 2+1/(sin^2theta)-(cos^2theta)/(sin^2theta)

The roots of the equation |(3x^(2),x^(2) + x cos theta + cos^(2) theta ,x^(2) + x sin theta + sin^(2) theta),(x^(2) + x cos theta + cos^(2) theta,3 cos^(2) theta,1 + (sin 2 theta)/(2)),(x^(2) + x sin theta + sin^(2) theta,1 + (sin 2 theta)/(2),3 sin^(2) theta)| = 0

If "cosec" theta = sqrt(5) , find the value of (i) 2-sin^(2)theta - cos^(2)theta (ii) 2 + (1)/(sin^(2)theta) - (cos^(2)theta)/(sin^(2)theta)

Prove that : (1+ sin theta - cos theta) / (1+ sin theta + cos theta ) = tan (theta/2)

Prove that (1- cos theta + sin theta)/( 1+cos theta +sin theta) = "tan"(theta)/(2) .

Find the value of (1+cos theta+sin theta)/(1-cos theta +sin theta)

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