Question

$Ifco{s}^{-1}\left(a\right)=\theta whereaϵ[-1,1]thenfindco{s}^{-1}(-a).$

• A. $\theta$
• B. $-\theta$
• C. Doesn't exist
• D. None of these

Answer 1

The correct option is D None of these

$Wehaveseenthatco{s}^{-1}\left(x\right)isneitheroddnoranevenfunction.\&co{s}^{-1}(-x)=\pi -co{s}^{-1}forallxϵ[-1,1]co{s}^{-1}\left(a\right)=\theta \left(Given\right)Then,co{s}^{-1}(-a)=\pi -co{s}^{-1}\left(a\right)Orco{s}^{-1}(-a)=\pi -\theta$