Aspire Faculty ID #14030 · Topic: JAMIA MILLIA ISLAMIA MCA 2019 · Just now
JAMIA MILLIA ISLAMIA MCA 2019

The value of $\tan\left(\frac{\pi}{8}\right)$ is:

Solution

$\tan\left(\frac{\pi}{8}\right) = \tan(22.5^\circ)$ Using the half–angle identity: $\tan\frac{\theta}{2} = \frac{1 - \cos\theta}{\sin\theta}$ For $\theta = \frac{\pi}{4}$, $\tan\frac{\pi}{8} = \frac{1 - \cos\frac{\pi}{4}}{\sin\frac{\pi}{4}} = \frac{1 - \frac{1}{\sqrt{2}}}{\frac{1}{\sqrt{2}}} = \sqrt{2} - 1.$

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