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NDA 2019 Maths · Mathematics · Trigonometric Functions and Identities · medium

If sin θ=1/3, then sin 3θ equals

Single correct option

If sin⁡θ=13\sin\theta=\dfrac13, then sin⁡3θ\sin3\theta equals
  1. A. 127\dfrac{1}{27}
  2. B. 2527\dfrac{25}{27}
  3. C. 2327\dfrac{23}{27}
  4. D. 11
Show answer and solution

Answer: (C) 2327\dfrac{23}{27}

Use sin⁡3θ=3sin⁡θ−4sin⁡3θ=3⋅13−4⋅127=1−427=2327\sin3\theta=3\sin\theta-4\sin^3\theta=3\cdot\dfrac13-4\cdot\dfrac1{27}=1-\dfrac4{27}=\dfrac{23}{27}. The value 11 results from forgetting the cubic term, and 127\dfrac1{27} from the confusion with sin⁡3θ\sin^3\theta. The identity must be recalled exactly, including the coefficient 44 and the minus sign.
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Original question written in the NDA 2019 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake