# the range of values of p for which the equation:sin cos¯¹(cos(tan¯¹x))=pans:[0,1) explain

Arun Kumar IIT Delhi
8 years ago
$sin(\cos^{-1}(cos(tan^{-1}x)))$

I'm assuming x belongs to Real No.

$tan^{-1}x \in [-\Pi/2,\Pi/2]$
so
$cos^{-1} \in [0,\Pi/2] \, since \,its\, input\, is\, +ve \,always$

going along we see here domain for sin will be
$[0,\Pi/2]$
so range is
$[0,1]$

Arun Kumar
IIT Delhi