The values of `alpha` for which the equation `alpha^2/(1-tan^2x)=(sin^2+xalpha^2-2)/(cos2x)` has solution can be

The values of alpha for which the equation alpha^2/(1-tan^2x)=(sin^2x+alpha^2-2)/(cos2x) has solution can be

The values of alpha for which the equation alpha^2/(1-tan^2x)=(sin^2x+alpha^2-2)/(cos2x) has solution can be

The values of alpha for which the equation alpha^2/(1-tan^2x)=(sin^2+alpha^2-2)/(cos2x) has solution can be

The range of alpha for which the equation sin^(4)x+cos^(4)x+sin2x+alpha=0 has solution

The number of values of alpha in [-10pi, 10pi] for which the equations (sin alpha)x-(cos alpha)y+3z=0, (cos alpha)x+(sin alpha)y-2z=0 and 2x+3y+(cos alpha)z=0 have nontrivial solution is

The number of values of alpha in [-10pi, 10pi] for which the equations (sin alpha)x-(cos alpha)y+3z=0, (cos alpha)x+(sin alpha)y-2z=0 and 2x+3y+(cos alpha)z=0 have nontrivial solution is

The set of values of alpha for which the equation "sin"^(4) x + "cos"^(4) x + "sin" 2x + alpha =0 possesses a solution, is

The minimum integral value of alpha for which the quadratic equation (cot^(-1)alpha)x^(2)-(tan^(-1)alpha)^(3//2)x+2(cot^(-1)alpha)^(2)=0 has both positive roots