Question

tan^1(tan7π/6)find the value
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Answer 1

Step-by-step explanation:

Question:-

$\tan {}^{ - 1} ( \tan( \frac{7\pi}{6} ) )$

Solution:-

$\tan {}^{ - 1} ( \tan( \frac{7\pi}{6} ) )$

convert into

$\small{(2n + 1)\pi + \theta}$

now

$\tan {}^{ - 1} ( \tan(\pi + \frac{\pi}{6} ) )$

its lies on 3rd quadrant in third quadrant cot and tan are +ve

$\tan {}^{ - 1} ( \tan( \frac{\pi}{6} ) )$

use property of inverse trigonometry

$\tan {}^{ - 1} ( \tan(x) ) = x$

use this property

$\tan {}^{ - 1} ( \tan( \frac{\pi}{6} ) ) \\ \implies \frac{\pi}{6}$

Answer:-

$\frac{\pi}{6}$