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NDA 2021
Exam
NDA
Year
2021
Subject
Mathematics
Chapter
Trigonometric Ratios & Identities

NDA 2021 · Mathematics · Trigonometric Ratios & Identities

If A=(1)/(7) , then what is 2 A equal to?

If tan⁡A=17\tan A=\frac{1}{7}, then what is cos⁡2A\cos 2 A equal to?

Options

  1. A2425\frac{24}{25}
  2. B1825\frac{18}{25}
  3. C1225\frac{12}{25}
  4. D625\frac{6}{25}

Correct answer

A. 2425\frac{24}{25}

Step-by-step solution

tan⁡A=17,cos⁡2A=1−tan⁡2A1+tan⁡2A=1−(17)21+(17)2=2425\tan A=\frac{1}{7}, \cos 2 A=\frac{1-\tan ^2 A}{1+\tan ^2 A}=\frac{1-\left(\frac{1}{7}\right)^2}{1+\left(\frac{1}{7}\right)^2}=\frac{24}{25}
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