Question

If $\beta$ satisfies the inequation $x^2-x-6>0$, then a value exists for

• A. ${\cos }^{-1}(\cos \beta )$
• B. $\sec ({\sec }^{-1}\beta )$
• C. ${\tan }^{-1}\beta$
• D. $\sin ({\sin }^{-1}\beta )$

Answer 1

Answer: (B), (C)

Since, : $\beta$ satisfy the inequation $x^2-x-6>0$
$\Rightarrow {\beta }^2-\beta -6>0$
$\Rightarrow (\beta -3)(\beta +2)>0$
$\Rightarrow \beta >3,\beta <-2$