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 $
$\Rightarrow \: \beta > 3, \beta < -2$