The value of tan left(frac{pi}{8}right) is | vedclass

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(A) We know the formula $	an \left(\frac{A}{2}ight) = \frac{1-\cos A}{\sin A}$.Putting $A = \frac{\pi}{4}$,we get $\frac{A}{2} = \frac{\pi}{8}$.The

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$\sqrt{2}-1$

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(A) We know the formula $	an \left(\frac{A}{2}ight) = \frac{1-\cos A}{\sin A}$.Putting $A = \frac{\pi}{4}$,we get $\frac{A}{2} = \frac{\pi}{8}$.Therefore,$	an \left(\frac{\pi}{8}ight) = \frac{1-\cos(\pi/4)}{\sin(\pi/4)}$.Substituting the values $\cos(\pi/4) = \frac{1}{\sqrt{2}}$ and $\sin(\pi/4) = \frac{1}{\sqrt{2}}$,we get:$	an \left(\frac{\pi}{8}ight) = \frac{1 - \frac{1}{\sqrt{2}}}{\frac{1}{\sqrt{2}}} = \frac{\frac{\sqrt{2}-1}{\sqrt{2}}}{\frac{1}{\sqrt{2}}} = \sqrt{2}-1$.

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

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