The number of all possible values of `theta`, where `0 lt theta lt pi`, for which the system of equations `(y+z)cos 3 theta =(xyz) sin 3 theta ,x sin 3 theta =(2cos3theta)/y+(2sin3theta)/z and (x y z)sin3theta=(y+2z)cos3theta+ysin3theta` have a solution `(x_0,y_0,z_0)` wiith `y_0 z_0 !=0` is

The number of all possible values of theta where 0 lt theta lt pi for which the system of equations (y+z)cos 3 theta=(xyz)sin 3theta, x sin 3 theta=(2cos 3theta)/y+(2sin 3 theta)/y, (xyz) sin 3theta=(y+2z)cos 3 theta+y sin 3 theta has a solution (x_(0),y_(0),z_(0)) with y_(0)z_(0)!=0 is

The number of all possible values of theta , where 0 lt theta lt pi , for which the system of equations (y+z) cos 3 theta = (xyz) sin 3 theta x sin 3 theta=(2 cos 3 theta)/y+(2 sin 3 theta)/z (xyz) sin 3 theta = (y+2z) cos 3 theta +y sin 3 theta has a solution (x_(0), y_(0), z_(0)) with y_(0)z_(0) ne 0 is _______.

The number of all possible values of theta, where 0

The number of all possible values of theta, where, for which the system of equations (y+z)cos3theta=(x y z)sin3theta xsin3theta=(2cos3theta)/y+(2sin3theta)/z (x y z)sin3theta=(y+2z)cos3theta+ysin3theta has a solution (x_0,y_0,z_0) with y_0z_0!=0 is

If 0 lt theta lt pi/2 , the solution of the equation sin theta - 3 sin 2 theta + sin 3 theta = cos theta - 3 cos 2 theta + cos 3 theta is

If x sin ^3 theta +y cos^3 theta = sin theta cos theta and x sin theta =y cos theta then x^2 +y^2 is

If x sin^3 theta+ y cos^3 theta = sin theta cos theta and x sin theta = y cos theta, Find the value of x^2 + y^2.

Solve the following systems of homogenous equations: {:(x cos theta - y sin theta = 0),(x sin theta + y cos theta = 0):}

x sin ^ (3) theta + y cos ^ (3) theta = sin theta cos theta and x sin theta = y cos theta Find the value of x ^ (2) + y ^ (2)