[" Q.No.11* "],[sin(tan^(-1)x),|x|<1" is equal to: "]

tan(sin^(-1)x)

Number of solutions of tan(sin^(-1)x)+sin(tan^(-1)x)=x is equal to

Column I: Function, Column II: Value of x for which both the functions in any option of column I are identical f(x)=tan^(-1)((2x)/(1-x^2)),g(x)=2tan^(-1)x , p. x in {-1,1} f(x)=sin^(-1)(sinx)a n dg(x)="sin"(sin^(-1)x) , q. x in [-1,1] f(x)=(log)_(x2)25a n dg(x)=(log)_x5 , r. x in (-1,1) f(x)=sec^(-1)x+cos e c^(-1)x ,g(x)=sin^(-1)x+cos^(-1)x , s. x in (0,1)

sin(tan^-1x), |x|<1 is equal to :

sin x = tan x11

lim_ (x rarr0) (sin (tan x) -tan (sin x)) / (tan ^ (- 1) (sin ^ (- 1) x) -sin ^ (- 1) (tan ^ (- 1) x )) =

(3 pi)/(2) The value of int_(0)^((3 pi)/(2))(|tan^(-1)tan x|-|sin^(-1)sin x|)/(|tan^(-1)tan x|+|sin^(-1)sin x|)dx is equal to

Value of sin{tan^(-1)x+tan^(-1)((1)/(x))}_( is )

sin(cot^(-1)(tan(tan^(-1)x))),x in(0,1]

sin(cot^(-1)(tan(tan^(-1)x))),"x" in (0," 1]