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3.Trigonometrical Ratios, Functions and Identities
medium
Find the value of $\tan \frac{13 \pi}{12}$
A
$ 2 - \sqrt 3 $
B
$2 - \sqrt 3 $
C
$ 2 - \sqrt 3 $
D
$ 2 - \sqrt 3 $
Solution
We have
$\tan \frac{{13\pi }}{{12}} = \tan \left( {\pi + \frac{\pi }{{12}}} \right)$
$ = \tan \frac{\pi }{{12}} = \tan \left( {\frac{\pi }{4} – \frac{\pi }{6}} \right)$
$ = \frac{{\tan \frac{\pi }{4} – \tan \frac{\pi }{6}}}{{1 + \tan \frac{\pi }{4}\tan \frac{\pi }{6}}}$
$ = \frac{{1 – \frac{1}{{\sqrt 3 }}}}{{1 + \frac{1}{{\sqrt 3 }}}} = \frac{{\sqrt 3 – 1}}{{\sqrt 3 + 1}}$
$= 2 – \sqrt 3 $
Standard 11
Mathematics
