How do you prove $sin^-1(-x)=-sin^-1x$ ?

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Answer 1 · 2016-10-12T16:06:34

see below

$sin^-1(-x)=-sin^-1x$

Let $y=-sin^-1x$

$-y=sin^-1x$

$sin(-y)=x$ by the inverse property

$-siny=x$ by the odd function property $sin(-x)=-sinx$

$siny = -x$

$y=sin^-1(-x)$

$:. -sin^-1x=sin^-1(-x)$

How do you prove sin^-1(-x)=-sin^-1xsin^-1(-x)=-sin^-1x?