`tan^(-1)x+cot^(-1)x=(pi)/(2) `holds when
(a) x in R (b) x in R-(-1 1) only (c) x in R-{0} only (d) x in R- -1 1 only

If |sin^(-1)x|+|cos^(-1)x|=(pi)/(2), then (a) x in R (b) [-1,1](c)[0,1](d)varphi

2 tan ( tan^(-1)(x)+ tan^(-1)(x^(3))) " where " x in R - {-1,1} is equal to

f(x)=2x-tan^(-1)x-log{x+sqrt(x^(2)+1)} is monotonically increasing when (a) x>0 (b) x<0( c) x in R( d ) x in R-{0}

if tan^(-1)x=(pi)/(10) for some x in R then the value of cot^(-1)x is

Is cot^(-1) (-x) = pi - cot^(-1) x , x in R

If f(x)=x^(1/3)(x-2)^(2/3) for all x, then the domain of f' is x in R-{0} b.{x|x:)0} c.x in R-{0,2} d.x in R

The function f(x)=(tan^(-1)x)^(3)-(cot^(-1)x)^(2)+tan^(-1)x+2 is (a)decreasing AA x in R( b)increasing AA x in R (c)bounded (d) Many one functions

Prove that (d)/(dx)(cot^(-1)x)=(-1)/((1+x^(2))) , where x in R .

It is given that A=(tan^(-1)x)^(3)+(cot^(-1)x)^(3) where x gt 0 and B=(cos^(-1)t)^(2)+(sin^(-1)t)^(2) where t in [0, (1)/(sqrt(2))] , and sin^(-1)x+cos^(-1)x=(pi)/(2) for -1 le x le 1 and tan^(-1)x +cot^(-1)x=(pi)/(2) for x in R . The maximum value of B is :

Assertion (A) : tan^(-1)x is ((-pi)/(2),(pi)/(2)) Reason (R ) : Domain of tan^(-1)x is R.