Question

why sin^-1(-x) is equal to - sin ^-1(x)

Answer 1

Step-by-step explanation:

Let $\sin^{-1}(x)=\theta$

Now,

$\sin( \theta) = \sin( \sin^{ - 1} (x) )$

$\implies \sin( \theta) = x$

Now,

$- x = - \sin( \theta)$

$\implies - x = \sin( - \theta)$

$\implies \sin^{ - 1} (- x) = \sin^{ - 1} (\sin( - \theta) )$

$\implies \sin^{ - 1} (- x) = - \theta$

$\implies \sin^{ - 1} (- x) = - \sin^{ - 1} (x)$