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NDA 2025 Maths · Mathematics · Trigonometric Functions and Identities · hard

The value of cos 12^°+cos 84^°+cos 156^°+cos 132^° is

Single correct option

The value of cos⁡12∘+cos⁡84∘+cos⁡156∘+cos⁡132∘\cos12^\circ+\cos84^\circ+\cos156^\circ+\cos132^\circ is
  1. A. 12\dfrac12
  2. B. 00
  3. C. 11
  4. D. −12-\dfrac12
Show answer and solution

Answer: (D) −12-\dfrac12

The angles are in AP with difference 72∘72^\circ (12,84,156,22812,84,156,228); note cos⁡132∘=cos⁡228∘\cos132^\circ=\cos228^\circ. Five angles at 72∘72^\circ spacing starting at 12∘12^\circ would sum to 00 (∑cos⁡=0\sum\cos=0), and the missing fifth term is cos⁡300∘=12\cos300^\circ=\frac12. So the four-term sum is −12-\frac12.
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Original question written in the NDA 2025 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