Q112 / 170 · Manipal (MET) 2019 · Mathematics

If $n \in N$, then $|\sin n x|$

  • A
    $\leq n|\sin x|$
  • B
    $\geq n|\sin x|$
  • C
    $=n|\sin x|$
  • Correct answer
    D
    None of these

Solution

$\begin{aligned} & \text { Let } \begin{aligned} T & =|\sin n x| \\ \text { Put } \quad n & =2 \text {, then } \\ T & =|\sin 2 x|=|2 \sin x \cos x| \leq 2|\sin x|\end{aligned}\end{aligned}$

Hence, the correct answer is option: 'D'.

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