The value of <span class="math-tex">\(\tan \left(\dfrac{7\pi}{8}\right)\)</span> is
\(\tan\frac{7\pi}{8} = \tan\left(\pi - \frac{\pi}{8}\right) = -\tan\frac{\pi}{8}\)
\(\tan\frac{\pi}{8} = \tan 22.5° = \sqrt{2} - 1\) (from \(\tan\frac{\theta}{2} = \frac{1 - \cos\theta}{\sin\theta}\) with \(\theta = 45°\)).
So \(\tan\frac{7\pi}{8} = -(\sqrt{2} - 1) = 1 - \sqrt{2}\).
Answer: (A)
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