Find real `theta` such that `(3+2i sin theta)/(1+2i sintheta)` is purely real.

Find theta such that (3+2i sin theta)/(1-2i sin theta) is purely real.

Prove that (1+tan^2theta)(1-sintheta)(1+sintheta)=1 .

Find sin 2 theta when sin theta + cos theta= 1 .

Find dy/dx when x = cos theta + cos 2 theta, y = sin theta + sin 2 theta)

Evaluate: int(tantheta)/(1-sintheta)d theta

If p tan theta = tan p theta , then show that : (sin^2 p theta)/(sin^2 theta)= (sin p^2)/(1+(p^2-1)sin^2 theta) .

Find all the values of theta for which the point (sin^2theta,sintheta) lies inside the square formed by the line x y=0 and 4x y-2x-2y+1=0.

If theta be any real, prove that : sin5 theta= 5sin theta-20 sin^3 theta+16 sin^5 theta .

Let f_(n)(theta)= 2 sin . (theta)/(2) sin. (3theta)/(2) + 2 sin.(theta)/(2) sin. (5theta)/(2) + 2sin. (theta)/(2) sin. (7 theta)/(2) + ... + 2 sin (2 n+1) (theta)/(2), n in N , then which of the following is/are correct ?

If x = 2 cos theta - cos 2 theta, y = 2 sin theta - sin 2 theta, find dy/dx at theta = pi/2