Question

Evaluate tan
$\frac{13\pi}{12}$
​

Answer 1

Step-by-step explanation:

the value of tan 13*π/12 = tan 195

= 0.2679

Answer 2

$\bigstar{\fbox{\mathfrak{\blue{\large{Answer:-}}}}}$

$\sf{We \:have}$

$\sf{\red{\tan \frac{13\pi}{12} = \tan(\pi + \frac{\pi}{12} )}}$

$\sf{\red{\tan\frac{\pi}{12} [\tan(\pi + 0) = \tan0]}}$

$\sf{\red{ \tan( \frac{\pi}{3} - \frac{\pi}{4} ) }}$

$\sf{\red{\frac{tan \frac{\pi}{3} - \tan \frac{\pi}{4} }{1 + tan \frac{\pi}{3} \tan \frac{\pi}{4} } = \frac{ \sqrt{3 } - 1}{1 + \sqrt{3} } }}$

$\sf{\red{(\frac{ \sqrt{3 } - 1}{1 + \sqrt{3} } ) \times (\frac{ \sqrt{3 } - 1}{1 - \sqrt{3} }) = \frac{ (\sqrt{3 } - {1})^{2} }{(3 - 1)}}}$

$\sf{\red{ \frac{(3 + 1 -2 \sqrt{3}) }{2} = \frac{(4 - 2 \sqrt{3}) }{2} = 2 - \sqrt{3} }}$