How do you prove $cot^-1x=tan^-1(1/x)$ for x>0?

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Answer 1 · 2016-10-12T15:43:19

see below

$cot^-1x=tan^-1(1/x)$

Let $y=cot^-1x$ , then by definition of inverse

$x=coty$

$x=1/tany$

$xtany=1$

$tany=1/x$

$y=tan^-1(1/x)$

$:. cot^-1x=tan^-1(1/x)$

How do you prove cot^-1x=tan^-1(1/x)cot^-1x=tan^-1(1/x) for x>0?