COMEDK · Maths · 2. Quadratic Equation
If \(\beta\) satisfies the inequation \(x^{2}-x-6>0\), then a value exists for
- A \(\cos ^{-1}(\cos \beta)\)
- B \(\sec \left(\sec ^{-1} \beta\right)\)
- C \(\tan \left(\tan ^{-1} \beta\right)\)
- D \(\sin \left(\sin ^{-1} \beta\right)\)
Answer & Solution
Correct Answer
(B) \(\sec \left(\sec ^{-1} \beta\right)\)
Step-by-step Solution
Detailed explanation
Since, \(\beta\) satisfy the inequation \[ \begin{array}{rlr} & & x^{2}-x-6>0 \\ \Rightarrow & & \beta^{2}-\beta-6>0 \\ \Rightarrow & & (\beta-3)(\beta+2)>0 \\ \Rightarrow & & \beta>3, \beta < -2 \end{array} \]
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