A solution of `sin^-1 (1) -sin^-1 (sqrt(3)/x^2)- pi/6 =0` is (A) `x=-sqrt(2)` (B) `x=sqrt(2)` (C) `x=2` (D) `x= 1/sqrt(2)`

The solution of sqrt(5-2sin x)>=6sin x-1 is

Solution set of inequation ( cos^-1x)^2-(sin^-1x)^2gt0 is (A) [0, 1/sqrt(2)) (B) [-1, 1/sqrt(2)) (C) (-1,sqrt2) (D) none of these

d/(dx)(sin^(-1)x+cos^(-1)x) is equal to : (A) (1)/(sqrt(1-x^(2))), (B) (2)/(sqrt(1-x^(2))), (C) 0 (D) sqrt(1-x^(2))

The number of solution of tan^-1(sqrt(x(x-1)))+sin^-1(sqrt(x^2+x+1))=pi/2 are

If sin^(-1) x + sin^(-1) y = pi/2 , prove that x sqrt(1-x^2) + y sqrt(1-y^2) =1 .

The number of the solutions of the equation 2 sin^(-1) sqrt(x^(2) + x + 1) + cos^(-1) sqrt(x^(2) + x) = (3pi)/(2) is