The Number Of Values Of x in The Interval [0, 3π] Satisfying The Equation 2sin2x + 5sinx – 3 = 0 Is:

The equation (cos p – 1)x² + (cos p)x + sin p = 0 where x is a variable, has real roots if p lies in the interval

The smallest positive number p for which the equation cos(p sinx) = sin(pcos x) has a solution x ∈ [0, 2π]

Number of solutions of pair x, y of the equation sin x sin y = min{–1, α² – 4α + 5}, α ∈ R (where 0 < x < π, – π < y < 0) is

  then sin x lies in

Number of solution of the equation 

Let α β ∈[– π π] be such that cos (α – β) = 1 and cos(α + β) = 1/e, The number of pairs of α, β satisfying the above system of equation is

The number of solution of the pair of equations 2sin²θ – cos2θ = 0 and 2cos²θ – 3sinθ = 0 in the interval [0, 2π] is

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

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