Find the value of `x` for which `sec^(-1)x+sin^(-1)x=pi/2dot`

Find the value of x for which f(x) = 2 sin^(-1) sqrt(1 - x) + sin^(-1) (2 sqrt(x - x^(2))) is constant

The value of x which satisfies sin^(-1)(1-x)-2sin^(-1)x=(pi)/(2) is (A) x=1 (B) x=(1)/(2)(C)x=0 (D) none of these

Find the value of cos(2cos^(-1)x+sin^(-1)x) at x=(1)/(5), where 0<=pi and -(pi)/(2)<=sin^(-1)x<=(pi)/(2)

Find the value of x for which the function f(x)=1+2sin x+3cos^(2)x(0<=x<=(2 pi)/(3)) ) is maximum.Also find these values of the function.

Find the values of p and q , for which f(x)={(1-sin^3x)/(3cos^2x)p(q(1-sinx)/((pi-2x)^2),ifx (pipi)/2 is continuous at x=pi/2dot

Find the value of x for which the following expression are defined (i) sin^(-1) (3x -2) (ii) cos^(-1) (log_(e) x) (iii) sec^(-1) (x^(2) -2)