Q250 / 270 · NDA 2018 (Phase 2) · Mathematics

What is $\lim _{x \rightarrow \frac{\pi}{6}} \frac{2 \sin ^2 x+\sin x-1}{2 \sin ^2 x-3 \sin x+1}$ to?

  • A
    -1/2
  • B
    -1/3
  • C
    -2
  • Correct answer
    D
    -3

Solution

$\lim _{x \rightarrow \frac{\pi}{6}} \frac{(\sin x+1)(2 \sin x-1)}{(\sin x-1)(2 \sin x-1)}=\frac{\frac{1}{2}+1}{\frac{1}{2}-1}=-3$

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

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