Question

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

Answer 1

this what i done so far
\[\sin ^{-1} -x =m\]
-x=sin m
x=-sin m

Answer 2

prove:
if \(f\) is odd, then \(f^{-1}\) is odd

Answer 3

sin(-x) = -sin(x) sin and tan are odd function
cos (-x) = cos(x) is even

Answer 4

do it without reference to any property of sine other than that it is odd, meaning \[\sin(-x)=-\sin(x)\]

Answer 5

thanks people

Answer 6

if sin (a) = x, then sin (-a) = -x, right?

Answer 7

yup

Answer 8

\(sin (a) = x \implies sin^{-1}(x) = a\)
\(sin(-a) = -x\implies sin^{-1}(-x) = -a\), OK?

Answer 9

ok

Answer 10

Hence from the first guy, you just multiple -1 both sides, you get \(-sin^{-1} (x) = -a\)
put it into the second one, you have what you want.