An Inequality with Sine and Cosine

★ 7/10trigonometrycalculusMonotonicityinequality

Problem

Let f(x)=x+sin⁡xf(x)=x+\sin x. If the inequality f(x)⩾axcos⁡xf(x)\geqslant ax\cos x holds for all x∈[0,π2]x\in\left[0,\dfrac{\pi}2\right], find the range of the real number aa.

Answer

Solution

Difficulty7/10
Topicstrigonometry, calculus, Monotonicity, inequality

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