A Solution (x, y) Of The System Of Equations    

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

The number of solutions of the pair of equations

         in the interval [0, 2π] is

 possesses a solution for

 cos x; u, v, w denote respectively sin²x, sin²y, sin²z, then the value of the triplet (u, v, w) is