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

Find sin theta . .

Find cos^2 theta - sin^2 theta . .

Find 1\(tan^2 theta) -1/(sin^2 theta) . .

Solve 2cos^2 theta+3 sin theta=0

Prove the following (1 + tan^2 theta)(1- sin ^2theta) = 1

Prove that sqrt((1-sin theta)/(1+sin theta))+sqrt((1+sin theta)/(1-sin theta))=-2/cos theta ,where pi/2ltthetaltpi .

Prove that cos theta/(1-sin theta)=tan (pi/4+theta/2)

lf 5 cos theta=7 sin theta , find the value of ( sin theta + cos theta)/(2 sin theta -3 cos theta) .

Find dy/dx : x = cos theta + sin theta, y = sin theta - theta cos theta

Is sin theta=1 = cos theta possible? Give reasons