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NDA 2022 Maths · Mathematics · Trigonometric Functions and Identities · medium

The value of cos 20^°+cos 100^°+cos 140^° is

Single correct option

The value of cos⁡20∘+cos⁡100∘+cos⁡140∘\cos20^\circ+\cos100^\circ+\cos140^\circ is
  1. A. 00
  2. B. 11
  3. C. 12\dfrac12
  4. D. −1-1
Show answer and solution

Answer: (A) 00

Use sum-to-product: cos⁡100∘+cos⁡140∘=2cos⁡120∘cos⁡20∘=−cos⁡20∘\cos100^\circ+\cos140^\circ=2\cos120^\circ\cos20^\circ=-\cos20^\circ. Adding cos⁡20∘\cos20^\circ gives 00. The trap is to evaluate each cosine numerically and round.
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Original question written in the NDA 2022 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