Q153 / 270 · NDA 2013 (Phase 2) · Mathematics

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

  • A
    1 < 4 < 2 < 3
  • Correct answer
    B
    4 < 2 < 1 < 3
  • C
    4 < 2 < 3 < 1
  • D
    1 < 4 < 3 < 2

Solution

From trigonometric values 1. $\tan \left(\frac{\pi}{6}\right)=\frac{1}{\sqrt{3}}$ 2. $\tan \left(\frac{3 \pi}{4}\right)=\tan \left(\pi-\frac{\pi}{4}\right)=\tan \left(\frac{\pi}{4}\right)=-1$ 3. $\tan \left(\frac{5 \pi}{4}\right)=\tan \left(\pi+\frac{\pi}{4}\right)=\tan \left(\frac{\pi}{4}\right)=1$ 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 $4 \lt 2 \lt 1 \lt 3$.

Hence, the correct answer is option: 'B'.

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