Question

The value of $\tan\left(\dfrac{7\pi}{8}\right)$ is

• A. $\sqrt{2} - 1$
• B. $1 - \sqrt{2}$
• C. $1 + \sqrt{2}$
• D. $\dfrac{1}{1 + \sqrt{2}}$

Hint:

Use identities like $\tan(\pi - x) = -\tan x$ and standard angle reductions for evaluating exact values.

Answer 1

The Correct Option is B

We use: $\tan\left(\dfrac{7\pi}{8}\right) = \tan\left(\pi - \dfrac{\pi}{8}\right) = -\tan\left(\dfrac{\pi}{8}\right)$
Now, $\tan\left(\dfrac{\pi}{8}\right) = \tan 22.5^\circ = \sqrt{2} - 1$
Hence, $\tan\left(\dfrac{7\pi}{8}\right) = -(\sqrt{2} - 1) = 1 - \sqrt{2}$