If `f(x)=sin^(-1)((sqrt(3))/2x-1/2sqrt(1-x^2)),-1/2lt=xlt=1,t h e nf(x)` is equal to

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

Range of f(x) =sin^-1(sqrt(x^2+x+1)) is

If y=cos^(-1)sqrt((sqrt(1+x^2)+1)/(2sqrt(1+x^2))),t h e n(dy)/(dx) is equal to (a) 1/(2(1+x^2)),x in R (b) 1/(2(1+x^2)),x >0 (c) (-1)/(2(1+x^2)),x<0 (d) 1/(2(1+x^2)),x<0

I ff(x)=2tan^(- 1)x+sin^(- 1)((2x)/(1+x^2)), x > 1 .T h e n , f(5) is equal to

y = sin ^(-1)(2xsqrt(1 - x^(2))),-(1)/sqrt(2) lt x lt (1)/sqrt(2)

int(e^x[1+sqrt(1-x^2)sin^-1x])/sqrt(1-x^2)dx

If the function f(x)=cos^(-1)(x^((3)/(2))-sqrt(1-x-x^(2)+x^(3))) (" where, "AA 0 lt x lt 1), then the value of |sqrt3f'((1)/(2))| is equal to ("take "sqrt3=1.73)

The value of tan^(-1)[(sqrt(1+x^2)+sqrt(1-x^2))/(sqrt(1+x^2)-sqrt(1-x^2))]=theta, |x|<1/2,x!=0 , is equal to:

If intsin^(-1)xcos^(-1)xdx=f^(-1)(x) [π/2x-xf^(-1)(x)-2sqrt(1-x^2)]+2x+C ,t h e n f(x)=sinx (b) f(x)=cosx A=pi/4 (d) A=pi/2

Show that(i) sin^(-1)(2xsqrt(1-x^2))=2sin^(-1)x ,-1/(sqrt(2))lt=xlt=1/(sqrt(2)) (ii) sin^(-1)(2xsqrt(1-x^2))=2cos^(-1)x ,1/(sqrt(2))lt=xlt=1