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NDA 2017 Maths · Mathematics · Trigonometric Functions and Identities · hard

The value of sin 10^°sin 30^°sin 50^°sin 70^° is

Single correct option

The value of sin⁡10∘sin⁡30∘sin⁡50∘sin⁡70∘\sin10^\circ\sin30^\circ\sin50^\circ\sin70^\circ is
  1. A. 18\dfrac1{8}
  2. B. 132\dfrac1{32}
  3. C. 116\dfrac1{16}
  4. D. 316\dfrac3{16}
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Answer: (C) 116\dfrac1{16}

Use sin⁡θsin⁡(60∘−θ)sin⁡(60∘+θ)=14sin⁡3θ\sin\theta\sin(60^\circ-\theta)\sin(60^\circ+\theta)=\frac14\sin3\theta with θ=10∘\theta=10^\circ: sin⁡10∘sin⁡50∘sin⁡70∘=14sin⁡30∘=18\sin10^\circ\sin50^\circ\sin70^\circ=\frac14\sin30^\circ=\frac18. Multiplying by sin⁡30∘=12\sin30^\circ=\frac12 gives 116\frac1{16}. The trap is forgetting the extra factor sin⁡30∘\sin30^\circ and answering 18\frac18.
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Original question written in the NDA 2017 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