Q67 / 150 · MHT CET 2026 (17 April Shift 2) · Mathematics

$\sin\left(3\sin^{-1}\left(\dfrac{1}{5}\right)\right) =$

  • A
    $\dfrac{74}{125}$
  • Correct answer
    B
    $\dfrac{71}{125}$
  • C
    $\dfrac{3}{5}$
  • D
    $\dfrac{1}{2}$

Solution

Let $\theta = \sin^{-1}\left(\dfrac{1}{5}\right)$.

Then, $\sin\theta = \dfrac{1}{5}$.

The given expression becomes $\sin(3\theta)$.

Using the identity $\sin(3\theta) = 3\sin\theta - 4\sin^3\theta$:

$\sin(3\theta) = 3\left(\dfrac{1}{5}\right) - 4\left(\dfrac{1}{5}\right)^3$

$\sin(3\theta) = \dfrac{3}{5} - \dfrac{4}{125}$

$\sin(3\theta) = \dfrac{75 - 4}{125}$

$\sin(3\theta) = \dfrac{71}{125}$

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

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