Find the value of tan frac{13 pi}{12}. | vedclass

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Question

(A) We have $	an \frac{13\pi}{12} = 	an \left( \pi + \frac{\pi}{12} ight)$.Since $	an(\pi + 	heta) = 	an 	heta$,we get $	an \frac{\pi}{12}$.N

Vedclass · Accepted Answer

$2 - \sqrt{3}$

Vedclass · Answer

(A) We have $	an \frac{13\pi}{12} = 	an \left( \pi + \frac{\pi}{12} ight)$.Since $	an(\pi + 	heta) = 	an 	heta$,we get $	an \frac{\pi}{12}$.Now,$\frac{\pi}{12} = \frac{\pi}{4} - \frac{\pi}{6} = 15^\circ$.Using the formula $	an(A - B) = \frac{	an A - 	an B}{1 + 	an A 	an B}$:$	an \left( \frac{\pi}{4} - \frac{\pi}{6} ight) = \frac{	an \frac{\pi}{4} - 	an \frac{\pi}{6}}{1 + 	an \frac{\pi}{4} 	an \frac{\pi}{6}} = \frac{1 - \frac{1}{\sqrt{3}}}{1 + 1 \cdot \frac{1}{\sqrt{3}}} = \frac{\sqrt{3} - 1}{\sqrt{3} + 1}$.Rationalizing the denominator:$\frac{(\sqrt{3} - 1)(\sqrt{3} - 1)}{(\sqrt{3} + 1)(\sqrt{3} - 1)} = \frac{3 - 2\sqrt{3} + 1}{3 - 1} = \frac{4 - 2\sqrt{3}}{2} = 2 - \sqrt{3}$.

Find the value of $\tan \frac{13 \pi}{12}$.

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