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Principal Solution of Trigonometric Equation

If α∈0, π/2, ...

Question

$I f α ϵ (0, \frac{π}{2}), t h e n \sqrt{x^{2} + x + \frac{t a n^{2} α}{\sqrt{x^{2} + x}}}$ is always greater than or equal to

A

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B

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C

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D

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Solution

The correct option is A

$\sqrt{x^{2} + x + \frac{t a n^{2} α}{\sqrt{x^{2} + x}}} \geq 2 t a n α (A . M \geq G . M) .$

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