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NDA 2013
Exam
NDA
Year
2013
Subject
Mathematics
Chapter
Trigonometric Ratios & Identities

NDA 2013 · Mathematics · Trigonometric Ratios & Identities

Consider the following: 1. ((π)/(6))2. ((3 π)/(4)) 3. ((5 π)/(4))...

Consider the following: 1. tan⁡(π6)2.\tan \left(\frac{\pi}{6}\right)2.\tan \left(\frac{3 \pi}{4}\right) 3. tan⁡(5π4)4.\tan \left(\frac{5 \pi}{4}\right) 4.\tan \left(\frac{2 \pi}{3}\right)

Options

  1. A1 < 4 < 2 < 3
  2. B4 < 2 < 1 < 3
  3. C4 < 2 < 3 < 1
  4. D1 < 4 < 3 < 2

Correct answer

B. 4 < 2 < 1 < 3

Step-by-step solution

From trigonometric values 1. tan⁡(π6)=132.tan⁡(3π4)=tan⁡(π−π4)=tan⁡(π4)=−13.tan⁡\tan \left(\frac{\pi}{6}\right)=\frac{1}{\sqrt{3}} 2. \tan \left(\frac{3 \pi}{4}\right)=\tan \left(\pi-\frac{\pi}{4}\right)=\tan \left(\frac{\pi}{4}\right)=-1 3. \tan\left(\frac{5 \pi}{4}\right)=\tan (π+π4)=tan⁡(π4)=14.tan⁡(2π3)=tan⁡(π−π3)=tan⁡(π3)=−3\left(\pi+\frac{\pi}{4}\right)=\tan \left(\frac{\pi}{4}\right)=1 4. \tan \left(\frac{2 \pi}{3}\right)=\tan \left(\pi-\frac{\pi}{3}\right)=\tan \left(\frac{\pi}{3}\right)=-\sqrt{3} Hence, correct ascending order is 4<2<1<34 < 2 < 1 < 3.
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