" If "sqrt(3)sin pi x+cos pi x=x^(2)-(2)/(3)x+(19)/(9)," then "x" is equal to : "

If sqrt(3)sin pi x+cos pi x=x^(2)-(2)/(3)x+(19)/(9) then x os equal to

if x+y=(2 pi)/(3) and cos x+cos y=(sqrt(3))/(2) then x,y is equal to:

Let 2y={(cot^(-1)(sqrt(3)cos x-sin x))/(cos x+sqrt(3)sin x))^(2) then (dy)/(dx) is equal to (A) x-(pi)/(6)(B)x+(pi)/(6)(C)2x-(pi)/(6)(D)2x-(pi)/(3)])

If 2y=(cot^(-1)((sqrt3 cos x + sin x)/(cos x - sqrt3 sin x)))^(2) , x in (0, pi/2) " then " (dy)/(dx) is equal to

If 2y=(cot^(-1)((sqrt3 cos x + sin x)/(cos x - sqrt3 sin x)))^(2) , x in (0, pi/2) " then " (dy)/(dx) is equal to

int _(0)^(pi//3) (cos x + sin x)/(sqrt(1+sin 2x))dx is equal to