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NDA 2017
Exam
NDA
Year
2017
Subject
Mathematics
Chapter
Trigonometric Ratios & Identities

NDA 2017 · Mathematics · Trigonometric Ratios & Identities

What is the value of 18^ ^ ?

What is the value of tan⁡18∘?\tan 18^{{}^{\circ}} ?

Options

  1. A5−110+25\frac{\sqrt{5}-1}{\sqrt{10+2 \sqrt{5}}}
  2. B5−110+5\frac{\sqrt{5}-1}{\sqrt{10+\sqrt{5}}}
  3. C10+255−1\frac{\sqrt{10+2 \sqrt{5}}}{\sqrt{5}-1}
  4. D10+55−1\frac{\sqrt{10+\sqrt{5}}}{\sqrt{5}-1}

Correct answer

A. 5−110+25\frac{\sqrt{5}-1}{\sqrt{10+2 \sqrt{5}}}

Step-by-step solution

tan⁡18∘=sin⁡18∘cos⁡18∘=5−1410+254=5−110+25\tan 18^{{}^{\circ}}=\frac{\sin 18^{{}^{\circ}}}{\cos 18^{{}^{\circ}}}=\frac{\frac{\sqrt{5}-1}{4}}{\frac{\sqrt{10+2 \sqrt{5}}}{4}}=\frac{\sqrt{5}-1}{\sqrt{10+2 \sqrt{5}}}
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