If `tan theta = (xsin phi)/(1-xcos phi)` and `tan phi = (y sin theta)/(1-y cos theta)` show that `x sin phi = y sin theta`

(sin theta + sin 2 theta)/( 1 + cos theta + cos 2 theta) = tan theta.

(sin ( theta -phi))/(sin theta sin phi) = cot phi - cot theta.

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

(sin (theta + phi))/( sin theta cos phi) = cot theta tan phi +1.

" If "|{:(sin theta cos phi,,sin theta sin phi,,cos theta),(cos theta cos phi,, cos theta sin phi,,-sin theta),(-sin theta sin phi,,sin theta cos phi,,theta):}| then

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

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

If y sinphi = x sin (2theta + phi) show that (x + y) cot (theta + phi) = (y-x) cot theta .

If the system of linear equations {:((cos theta)x + (sin theta) y + cos theta=0),((sin theta)x+(cos theta)y + sin theta=0),((cos theta)x + (sin theta)y -cos theta=0):} is consistent , then the number of possible values of theta, theta in [0,2pi] is :

If 5 tan theta = 4 , show that ( 5 sin theta - 3 cos theta)/(5 sin theta + 3 cos theta) = (1)/(7)