Question

$If-1⩽a⩽1,thensi{n}^{-1}\left(a\right)+co{s}^{-1}\left(a\right)isequalto-$

• A. 1
• B. $\pi$
• C. $\frac{\pi }{2}$

Answer 1

The correct option is C $\frac{\pi }{2}$

$Letsi{n}^{-1}\left(a\right)=yBeforeassumingsuchthingswehavetocheckcertainconditions.Giventhat-1\le a\le 1Thuswecanassumesi{n}^{-1}\left(a\right)=y,asthedomainofsi{n}^{-1}\left(x\right)canbe[-1,1].So,si{n}^{-1}\left(a\right)=y;-\frac{\pi }{2}\le y\le \frac{\pi }{2}or,a=sin\left(y\right)Also,a=cos(\frac{\pi }{2}-y)\frac{\pi }{2}-y=co{s}^{-1}\left(a\right)\left(Wecouldwritethisequationbecauseaϵ\right[-1,1]-yϵ[0,\pi \left]\right)\frac{\pi }{2}=co{s}^{-1}\left(a\right)+y=si{n}^{-1}\left(a\right)+co{s}^{-1}\left(a\right)=\frac{\pi }{2}(Since,si{n}^{-1}(a)=y)$