If n be The Number Of Solutions Of The Equation   

If sin 3α = 4 sin α sin (x + α) sin (x – α), then 864 sin² x + 3620 cos² x is equal to.

If x and y are the solution of the equation 12 sin x + 5 cos x + 5 cos x = 2y² – 8y + 21, the value of 3864 cot (xy/2) is

The number of values of x in the interval [0, 3π] satisfying the equation 2sin²x + 5sinx – 3 = 0 is:

If 2sin²θ – 5sinθ + 2 > 0, θ ∈ (0, 2π), then θ ∈:

The number of solutions of the pair of equations   

     2sin²θ – cos2θ = 0   

    2cos²θ – 3sin θ = 0     

In the interval [0, 2π] is

If  are the smallest +ive angles n ascending order of magnitude which have their sines equal to a +ive quantity λ then the value of  

The equation a sinx + cos2x = 2a – 7 possesses a solution if

The number of values of x in the interval [0, 5π] satisfying the equation 3sin²x – 7sin x + 2 = 0 is

The number of solutions of the equation tan x.tan 4x = 1 for 0 < x < π is

The values of x between 0 and 2π which satisfy the equation

 are in A.P. The common difference of the A.P. is