Q245 / 270 · NDA 2018 (Phase 1) · Mathematics

What is $\lim _{x \rightarrow 0} \frac{\tan x}{\sin 2 x}$ equal to?

  • Correct answer
    A
    $\frac{1}{2}$
  • B
    $1$
  • C
    2
  • D
    Limit does not exist

Solution

$\lim _{x \rightarrow 0} \frac{\tan x}{\sin 2 x}=\lim _{x \rightarrow 0} \frac{\frac{\tan x}{x}}{2\left(\frac{\sin 2 x}{2 x}\right)}=\frac{1}{2}$

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

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