# If cos-1x=tan-1x then prove that the following sin(cos-1x)=x2

$Let\quad \cos ^{ -1 }{ x\quad =\quad \tan ^{ -1 }{ x\quad = } y } \\ Implies\quad \cos { y } =\quad x\quad and\quad tany\quad =x\\ \frac { siny }{ cosy } =\quad x\quad Put\quad cosy\quad =\quad x\\ \frac { siny }{ x } =\quad x\\ siny\quad =\quad { x }^{ 2 }\quad put\quad y\quad =\quad \cos ^{ -1 }{ x\quad we\quad have } \\ sin\quad (\cos ^{ -1 }{ x)\quad =\quad } { x }^{ 2 }$