Q198 / 270 · NDA 2022 (Phase 2) · Mathematics

What is the value of $\tan \left(\frac{3 \pi}{8}\right)$ ?

  • A
    $\sqrt{2}-1$
  • Correct answer
    B
    $\sqrt{2}+1$
  • C
    $1-\sqrt{2}$
  • D
    $-(\sqrt{2}+1)$

Solution

$\because \quad \tan \left(\frac{3 \pi}{4}\right)=\tan \left(\pi-\frac{\pi}{4}\right)=-1$ Let $\frac{3 \pi}{4}=\theta \quad \Rightarrow \quad \tan \theta=-1$ Now, $\tan \theta=\frac{2 \tan \theta / 2}{1-\tan ^2 \theta / 2}$ Let $\tan \theta / 2=x$ $\begin{aligned} & \therefore \quad-1=\frac{2 x}{1-x^2} \\ & \Rightarrow \quad x^2-2 x-1=0 \quad \Rightarrow \quad x=1 \pm \sqrt{2} \\ & \therefore \quad \tan \frac{3 \pi}{8}=1+\sqrt{2} \quad\left(\because 0 \lt \frac{3 \pi}{8} \lt \frac{\pi}{2}\right) \end{aligned}$

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

Relevant Questions