Fill `cot^(-1)(1/x)=...... (x gt 0)`

lim_(x rarr0)(cot^(-1)(1/x))/(x)

Solve (x-1 )(x-2)(1-2x) gt 0

Find the value of tan^(-1)(-x)-cot^(-1)(-1/x),x gt0

Find lim_(xto0)(cot^(-1)(1/x))/x

Prove that sin (cot^(-1) (tan (cos^(-1) x))) = x, x gt 0

Solve (x-1)(x-2)(1-2x) gt 0 .

If x gt y gt z gt 0 , then find the value of "cot"^(-1) (xy + 1)/(x - y) + "cot"^(-1)(yz + 1)/(y - z) + "cot"^(-1)(zx + 1)/(z - x)

STATEMENT -1 : The value of tan^(-1)x+tan^(-1)(1/x)=pi/2, AA x in R -{0} . and STATEMENT -2 : The value of tan^(-1).(1/x)={:{(cot^(-1)x,x gt0),(-pi+cot^(-1)x,x lt0):}

2x ^ (2) + (1) / (x)> 0

cot(tan^(-1)x+cot^(-1)x)