Question

The complete solution set of the inequality $\left(cos\right)^{- 1} \left(\right. cos 4 \left.\right) > 3 x^{2} - 4 x \, $ is

• A. $\left(0 , \frac{2 + \sqrt{6 \pi - 8}}{3}\right)$
• B. $\left(\frac{2 - \sqrt{6 \pi - 8}}{3} , 0\right)$
• C. $\left(\right.-2, 2\left.\right)$
• D. $\left(\frac{2 - \sqrt{6 \pi - 8}}{3} , \frac{2 + \sqrt{6 \pi - 8}}{3}\right)$

Answer 1

Answer: (D)

As, $\left(cos\right)^{- 1} \left(\right. cos ⁡ 4 \left.\right) = \left(cos\right)^{- 1} ⁡ \left\{cos ⁡ \left(2 \pi - 4\right)\right\} = 2 \pi - 4$
$⇒ \, \, \, 2\pi -4>3x^{2}-4x$
$⇒ \, \, \, 3x^{2}-4x-\left(2 \pi - 4\right) < 0$
$⇒ \, \, \, \frac{2 - \sqrt{6 \pi - 8}}{3} < x < \frac{2 + \sqrt{6 \pi - 8}}{3}$