≤ft(3 ^{-1}≤ft(1/5))=

Correct Answer is : 7112571/12512571

Correct Answer is : 7112571/12512571

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MHTCET 17 Apr 2026 Shift 2 Paper

Question : 115 of 150

Marks: +1, -0

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

Solution:

Concept:

Use the triple-angle identity for sine after substituting the inverse sine value.

Explanation:

Let

\theta = \sin^{-1}\left(\frac{1}{5}\right)

Then

\sin \theta = \frac{1}{5}

The given expression becomes

\sin(3\theta)

Use the identity:

\sin 3\theta = 3\sin\theta - 4\sin^3\theta

Substitute

\sin\theta = \frac{1}{5}

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

= \frac{3}{5} - \frac{4}{125} = \frac{75 - 4}{125} = \frac{71}{125}

Therefore, the value of the expression is

\frac{71}{125}

Answer:

Option B,

\frac{71}{125}

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