Question

If $tan3x=\sin {45}^0\cos {45}^0+\sin {30}^0$, find the value of X.

Answer 1

$\tan 3x=\frac{1}{\sqrt{2}}\times \frac{1}{\sqrt{2}}+\frac{1}{2}$

$=\frac{1}{2}+\frac{1}{2}=1$

$\Rightarrow \tan 3x=1$

$\Rightarrow 3x=n\pi +\frac{\pi }{4}$

$\therefore x=\frac{n\pi }{3}+\frac{\pi }{12}$ for $n\in Z$