MCQ
If $\alpha \in \left( {0,\,\frac{\pi }{2}} \right),$ then $\sqrt {{x^2} + x} + \frac{{{{\tan }^2}\alpha }}{{\sqrt {{x^2} + x} }}$ is always greater than or equal to
  • $2\,\,\tan \alpha $
  • B
    $1$
  • C
    $2$
  • D
    ${\sec ^2}\alpha $

Answer

Correct option: A.
$2\,\,\tan \alpha $
a
(a) $\sqrt {{x^2} + x} + \frac{{{{\tan }^2}\alpha }}{{\sqrt {{x^2} + x} }} \ge 2\tan \alpha $ $({\rm{A}}{\rm{.M}}{\rm{.}} \ge {\rm{G}}{\rm{.M}}{\rm{.}}).$

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