Q78 / 160 · AP EAMCET 2020 (18 Sep Shift 2) · Mathematics

\(\frac{\sqrt{3} \sin (\theta)+\cos (\theta)}{\sin \left(\theta+\frac{\pi}{6}\right)}=\)

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

Solution

\(\begin{aligned} \frac{\sqrt{3} \sin \theta+\cos \theta}{\sin \left(\theta+\frac{\pi}{6}\right)} & =\frac{\sqrt{3} \sin \theta+\cos \theta}{\sin \theta \cos \frac{\pi}{6}+\cos \theta \sin \frac{\pi}{6}} \\ & =\frac{\sqrt{3} \sin \theta+\cos \theta}{\frac{\sqrt{3}}{2} \sin \theta+\frac{1}{2} \cos \theta}=2 \end{aligned}\) Hence, option (c) is correct.

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

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