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

The value of cos ^210^°+cos ^250^°+cos ^270^° is

Single correct option

The value of cos⁡210∘+cos⁡250∘+cos⁡270∘\cos^210^\circ+\cos^250^\circ+\cos^270^\circ is
  1. A. 11
  2. B. 34\dfrac34
  3. C. 32\dfrac32
  4. D. 22
Show answer and solution

Answer: (C) 32\dfrac32

Using cos⁡2θ=1+cos⁡2θ2\cos^2\theta=\frac{1+\cos2\theta}{2}, the sum is 32+12(cos⁡20∘+cos⁡100∘+cos⁡140∘)\frac32+\frac12(\cos20^\circ+\cos100^\circ+\cos140^\circ). Since cos⁡100∘+cos⁡140∘=2cos⁡120∘cos⁡20∘=−cos⁡20∘\cos100^\circ+\cos140^\circ=2\cos120^\circ\cos20^\circ=-\cos20^\circ, the bracket is 0. The sum is 32\frac32.
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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