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)#