[[" (a) "3x],[" (c) "cos^(-1)3x]" (d) None of the "x],[" the "sin^(-1)((sqrt(1+x)+sqrt(1-x))/(2))=?]

If x in[(sqrt(3))/(2), 1] then [sin^(-1){(x)/(sqrt(2))+(sqrt(1-x^(2)))/(sqrt(2))}-sin^(-1)x]=

Find the domain of the following following functions: (a) f(x)=(sin^(-1))/(x) (b) f(x)=sin^(-1)(|x-1|-2) (c ) f(x)=cos^(-1)(1+3x+2x^(2)) (d ) f(x)=(sin^(-1)(x-3))/(sqrt(9-x^(2))) (e ) f(x)="cos"^(-1)((6-3x)/(4))+"cosec"^(-1)((x-1)/(2)) (f) f(x)=sqrt("sec"^(-1)((2-|x|)/(4)))

If x takes negative permissible values , then sin^(-1) x= a) cos^(-1)sqrt(1-x^2) b) -cos^(-1)sqrt(1-x^2) c) cos^(-1)sqrt(x^2-1) d) pi-cos^(-1)sqrt(1-x^2)

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

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))

If x<0,t h e ntan^(-1)x is equal to -pi+cot^(-1)1/x (b) sin^(-1)x/(sqrt(1+x^2)) -cos^(-1)1/(sqrt(1+x^2)) (d) -cos e c^(-1)(sqrt(1+x^2))/x

If x<0,t h e ntan^(-1)x is equal to -pi+cot^(-1)1/x (b) sin^(-1)x/(sqrt(1+x^2)) -cos^(-1)1/(sqrt(1+x^2)) (d) -cos e c^(-1)(sqrt(1+x^2))/x

The domain of f(x)=sqrt(sin^(-1)(3x-4x^(3)))+sqrt(cos^(-1)x) is equal to

The domain of f(x)=sqrt(sin^(-1)(3x-4x^(3)))+sqrt(cos^(-1)x) is equal to