If the quadratic equation in `x, (2sin^2 theta)x^2-3x+2cos^2 tehta=0` and `(cos2theta)x^2-3x+sqrt3 sin2theta=0` have both roots common, then number of possible values of `theta` in `[-pi/2, (5pi)/2]` is equal to

One root of the quadratic equation sin^(2)theta x^(2)-x+cos^(2)theta=0 is given by

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 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 :

Solve the equation for 0 le x le 2pi. 2 sin ^(2) theta = 3 cos theta

If 2sin^(2)theta=3cos theta, where 0<=theta<=2 pi, then find the value of theta

Consider the cubic equation x^(3)-(1+cos theta+sin theta)x^(2)+(cos theta sin theta +cos theta + sin theta)x - sin theta cos theta =0 . When roots are x_(1),x_(2) and x_(3) . Number of values of theta in [0,2pi] for which at least two roots are equal

Let system of liner equations in x,y,z,xsin2theta-ycos2theta-zcos2theta=0x/(y z)sin2theta-(2sin2theta)/z-(2cos2theta)/y=0xsin2theta-y(sin2theta+cos2theta)-2zcos2theta=0has a non-trivial solution , then number of value (s) of theta in the interval [0, pi] is

The number of solutions of the pair of equations 2sin^2 theta - cos(2 theta)=0,2cos^2 theta-3sin theta=0 in the interval [0,2pi] is

The number of solutions of the pair of equations 2sin^2 theta - cos(2 theta)=0,2cos^2 theta-3sin theta=0 in the interval [0,2pi] is

The number of solutions of the pair of equations 2sin^2 theta - cos(2 theta)=0,2cos^2 theta-3sin theta=0 in the interval [0,2pi] is