Question

Find the value tan 31pie /3
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Answer 1

$\star\:\:\:\sf\large\underline\blue{Question:-}$

• Find the value of $\sf \tan( \frac{31\pi}{3} )$

$\star\:\:\:\sf\large\underline\blue{Solution::}$

$\sf \tan( \frac{31\pi}{3} )$

$\sf = \tan( \frac{30 \pi+ \pi}{3} )$

$\sf = \tan( \frac{\pi}{3} + 10\pi)$

We know that,

$\sf \tan(t \pm k \times \pi) = \tan(t),k \in \Z$

So,

$\sf = \tan( \frac{\pi}{3} + 10\pi)$

$\sf = \tan( \frac{\pi}{3} )$

$\sf = \sqrt{3}$

$\star\:\:\:\sf\large\underline\blue{Answer:-}$

• $\sf \tan( \frac{31\pi}{3} ) = \sqrt{3}$