(ii)(sin x)^(x)+sin^(-1)sqrt(x)

"Differentiate: "(sin x)^(x)+sin^(-1)sqrt(x)

sin^(-1)[sqrt(x^(2)-x^(3))-sqrt(x-x^(3))]=..... a) sin^(-1)x+sin^(-1)sqrt(x) b) sin^(-1)x-sin^(-1)sqrt(x) c) sin^(-1)sqrt(x)-sin^(-1)x d) 2sin^(-1)x

intsqrt(x/(1-x))\ dx is equal to (a) sin^(-1)sqrt(x)+C (b) sin^(-1){sqrt(x)-sqrt(x(1-x))}+C (c) sin^(-1){sqrt(x(1-x))}+C (d) sin^(-1)sqrt(x)-sqrt(x(1-x))+C

int sqrt((x)/(1-x))dx is equal to sin^(-1)sqrt(x)+C(b)sin^(-1){sqrt(x)-sqrt(x(1-x))}+C(c)sin^(-1){sqrt(x(1-x)}+C(d))sin^(-1)sqrt(x)-sqrt(x(1-x))+C

If sin^(-1)x+sin^(-1)(1-x)=sin^(-1)sqrt(1-x^(2)), then x is equal to

(sin^(-1)sqrt(x)-cos^(-1)sqrt(x))/(sin^(-1)sqrt(x)+cos^(-1)sqrt(x)),x in[0,1]

Solve for x : i) cos(sin^(-1)x)=1/2 ii) tan^(-1)x=sin^(-1)1/sqrt(2) iii) sin^(-1)x-cos^(-1)x=pi/6

Find the domain of each of the following functions: f(x)=sin^(-1)sqrt(x^2-1) (ii) f(x)=sin^(-1)x+sin^(-1)2x

Evaluate: int(sin^(-1)sqrt(x)-cos^(-1)sqrt(x))/(sin^(-1)sqrt(x)+cos^(-1)sqrt(x))\ dx