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NDA 2021 Maths · Mathematics · Trigonometric Functions and Identities · hard

The value of cos 12^°cos 24^°cos 48^°cos 96^° is

Single correct option

The value of cos⁡12∘cos⁡24∘cos⁡48∘cos⁡96∘\cos12^\circ\cos24^\circ\cos48^\circ\cos96^\circ is
  1. A. 116\dfrac1{16}
  2. B. 18\dfrac18
  3. C. −116-\dfrac1{16}
  4. D. −18-\dfrac18
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Answer: (C) −116-\dfrac1{16}

Multiply and divide by sin⁡12∘\sin12^\circ and use 2sin⁡θcos⁡θ=sin⁡2θ2\sin\theta\cos\theta=\sin2\theta four times: the product is sin⁡192∘16sin⁡12∘\dfrac{\sin192^\circ}{16\sin12^\circ}. As sin⁡192∘=−sin⁡12∘\sin192^\circ=-\sin12^\circ, the value is −116-\dfrac1{16}.
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Original question written in the NDA 2021 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