Question:
The value of
\[
\tan\left(\frac{7\pi}{8}\right)
\]
is
The value of
\[
\tan\left(\frac{7\pi}{8}\right)
\]
is
Show Hint
Remember the identity:
\[
\tan(\pi-\theta)=-\tan\theta
\]
Also,
\[
\tan\left(\frac{\pi}{8}\right)=\sqrt{2}-1
\]
is a standard trigonometric value.
Updated On: Jun 22, 2026
- \(\sqrt{2}-1\)
- \(1-\sqrt{2}\)
- \(1+\sqrt{2}\)
- \(\dfrac{1}{1+\sqrt{2}}\)
Show Solution
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The Correct Option is B
Solution and Explanation
Step 1: Rewrite the angle.
We have \[ \frac{7\pi}{8} = \pi-\frac{\pi}{8} \] Using the identity \[ \tan(\pi-\theta)=-\tan\theta, \] we get \[ \tan\left(\frac{7\pi}{8}\right) = -\tan\left(\frac{\pi}{8}\right) \]
Step 2: Find the value of \(\tan\left(\frac{\pi}{8}\right)\).
Using the standard identity, \[ \tan\left(\frac{\pi}{8}\right) = \sqrt{2}-1 \] Therefore, \[ \tan\left(\frac{7\pi}{8}\right) = -(\sqrt{2}-1) \] \[ =1-\sqrt{2} \]
Step 3: Final conclusion.
Hence, \[ \boxed{1-\sqrt{2}} \] which corresponds to option (2).
We have \[ \frac{7\pi}{8} = \pi-\frac{\pi}{8} \] Using the identity \[ \tan(\pi-\theta)=-\tan\theta, \] we get \[ \tan\left(\frac{7\pi}{8}\right) = -\tan\left(\frac{\pi}{8}\right) \]
Step 2: Find the value of \(\tan\left(\frac{\pi}{8}\right)\).
Using the standard identity, \[ \tan\left(\frac{\pi}{8}\right) = \sqrt{2}-1 \] Therefore, \[ \tan\left(\frac{7\pi}{8}\right) = -(\sqrt{2}-1) \] \[ =1-\sqrt{2} \]
Step 3: Final conclusion.
Hence, \[ \boxed{1-\sqrt{2}} \] which corresponds to option (2).
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