The Number Of Solutions Of The Pair Of Equations          in The Interval [0, 2π] 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

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 solution of 

The smallest positive number p for which the equation

          has a solution 

Number of solutions of pair x, y of the equation sin x sin y = min

{ –1, α² – 4α + 5}, α Ïµ R 

The number of solutions of the equation tan²x – sec¹⁰x + 1 = 0 in (0, 10) is

Number of solutions of the equation 

 be such that cos (α – β) = 1 and  = 1/e, The number of pairs of α, β satisfying the above system of equations is

 possesses a solution for