The number of all possible values of θ where 0 < θ < π, for which the system of equations `(y + z)cosθ = (xyz)sin3θ`
`sin3θ = 2cos((3θ)/y )+ 2sin((3θ)/z)`
`(xyz)sin3θ = (y + 2z)cos3θ + ysin3θ`
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 =(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 distinct solutions of secθ+tanθ= √3 , 0≤θ≤3π , is

cos^2θ - sinθ - 1/4 =0

Prove: sin^2θ + cos^2θ =1

The hybridisation number of lone pair of electron and shape of I_(3)^(Θ) is .

Prove that sin (x + y ) sin (x -y) + sin ( y+ z) sin (y - z) + sin (z+x) sin (z-x) = 0.

tan θ =-4/3 , sin θ is

Find the value of θ if cos theta=sqrt(3)(1-sin theta)

Find the value of θ of the following if cos theta-sqrt(3)sin theta=1

The number of solutions of equations x + y - z=0, 3x - y - z= 0,x - 3y + z = 0 is