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NDA 2019
Exam
NDA
Year
2019
Subject
Mathematics
Chapter
Trigonometric Ratios & Identities

NDA 2019 · Mathematics · Trigonometric Ratios & Identities

What is 80^ ^ + 40^ ^ - 20^ ^ equal to?

What is cos⁡80∘+cos⁡40∘−cos⁡20∘\cos 80^{{}^{\circ}}+\cos 40^{{}^{\circ}}-\cos 20^{{}^{\circ}} equal to?

Options

  1. A2
  2. B1
  3. C0
  4. D-19

Correct answer

C. 0

Step-by-step solution

∵cos⁡C+cos⁡D=2cos⁡(C+D2)⋅cos⁡(C−D2)⇒cos⁡80∘+cos⁡40∘=2cos⁡60∘⋅cos⁡20∘=2⋅12⋅cos⁡20∘=cos⁡20∘∴cos⁡80∘+cos⁡40∘−cos⁡20∘=0\begin{aligned} & \because \cos C+\cos D \\ & =2 \cos \left(\frac{C+D}{2}\right) \cdot \cos \left(\frac{C-D}{2}\right) \\ & \Rightarrow \cos 80^{{}^{\circ}}+\cos 40^{{}^{\circ}} \\ & =2 \cos 60^{{}^{\circ}} \cdot \cos 20^{{}^{\circ}} \\ & =2 \cdot \frac{1}{2} \cdot \cos 20^{{}^{\circ}}=\cos 20^{{}^{\circ}} \\ & \therefore \quad \cos 80^{{}^{\circ}}+\cos 40^{{}^{\circ}}-\cos 20^{{}^{\circ}}=0\end{aligned}
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