Q89 / 180 · KCET 2021 · Mathematics

$\cos \left[\cot ^{-1}(-\sqrt{3})+\frac{\pi}{6}\right]$ is equal to

  • A
    0
  • B
    1
  • C
    $\frac{1}{\sqrt{2}}$
  • Correct answer
    D
    $-1$

Solution

Given, $\begin{aligned} &\cos \left[\cot ^{-1}(-\sqrt{3})+\frac{\pi}{6}\right] \\ &=\cos \left[\pi-\cot ^{-1}(\sqrt{3})+\frac{\pi}{6}\right] \\ &=\cos \left[\pi-\frac{\pi}{6}+\frac{\pi}{6}\right] \\ &=\cos [\pi]=-1 \end{aligned}$

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

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