Column I, Column II `(a)sin^(-1)x+x >0,` `(p) x<0` `(b)cos^(-1)x-x >0,` `(q) x in [0,1]` `(c)tan^(-1)x+x >0,` `(r) x in [-1,0]` `(d)cot^(-1)x+x >0,` `(s) x >0`

Iff(x)={sin^(-1)(sinx),x >0, pi/2,x=0,tcos^(-1)(cosx),x<0

If x gt 0 , then tan^-1 x =

Solve sin^(-1) (sin 6x) = x, x in [0,pi]

Prove that sin cot^(-1) tan cos^(-1) x = sin cosec^(-1) cot tan^(-1) x = x, " where " x in [0,1]

int_(0)^(1)cot^(-1)(1-x+x^(2))dx

int_(0)^(1)tan^(-1)(1-x+x^(2))dx

Column I, Column II Range of f(x)=sin^(-1)x+cos^(-1)x+cot^(-1)xi s , p. [0,pi/2]uu[pi/2,pi] Range of f(x)= cot^(-1)x+tan^(-1)x+cos e c^(-1)xi s , q. [pi/2,(3pi)/2] Range of f(x)=cot^(-1)x+tan^(-1)x+cos^(-1)xi s , r. [0,pi] Range of f(x)= sec^(-1)x+cos e c^(-1)x+sin^(-1)xi s , s. [(3pi)/4,(5pi)/4]

lim_(x to 0) tan^-1x/x

f(x)=tan^(-1)x+tan^(-1)(1/x);g(x)=sin^(-1)x+cos^(-1)x are identical functions if (A) x in R (B) x >0 (C) x in [-1,1] (D) x in (0,1]

For all x in (0,1) (a) e^x (b) (log)_e (1+x) (c) sin x > x (d) (log)_e x > x