Find the value of $\tan \frac{13 \pi}{12}$
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 $
If $\tan x=\frac{3}{4}, \pi < x < \frac{3 \pi}{2},$ find the value of $\sin \frac{x}{2}, \cos \frac{x}{2}$ and $\tan \frac{x}{2}$
Let $A, B$ and $C$ are the angles of a plain triangle and $\tan \frac{A}{2} = \frac{1}{3},\,\,\tan \frac{B}{2} = \frac{2}{3}$. Then $\tan \frac{C}{2}$ is equal to
Find the radius of the circle in which a central angle of $60^{\circ}$ intercepts an arc of length $37.4 \,cm$ ( use $\pi=\frac{22}{7}$ ).
If $a\,{\cos ^3}\alpha + 3a\,\cos \alpha \,{\sin ^2}\alpha = m$ and $a\,{\sin ^3}\alpha + 3a\,{\cos ^2}\alpha \sin \alpha = n,$ then ${(m + n)^{2/3}} + {(m - n)^{2/3}}$ is equal to
If $\frac{\sin ^4 x}{2}+\frac{\cos ^4 x}{3}=\frac{1}{5},$ then
$(A)$ $\tan ^2 x=\frac{2}{3}$ $(B)$ $\frac{\sin ^8 x}{8}+\frac{\cos ^8 x}{27}=\frac{1}{125}$
$(C)$ $\tan ^2 x=\frac{1}{3}$ $(D)$ $\frac{\sin ^8 x}{8}+\frac{\cos ^8 x}{27}=\frac{2}{125}$