Answer
$3-\dfrac{3\sqrt 3}{2}$
Work Step by Step
We know that:
$\csc x=\dfrac{1}{\sin x}$
We also know that the trigonometric functions have the values
$\cos \dfrac{\pi}{6} =\dfrac{\sqrt 3}{2} ; \tan \dfrac{\pi}{4}=1; \sin \dfrac{\pi}{6}=\dfrac{1}{2}$
We evaluate the given expression to obtain:
$ \tan ( \dfrac{\pi}{4}) -3 \cos (\dfrac{\pi}{6})+\csc (\dfrac{\pi}{6})=1-3 \times (\dfrac{\sqrt 3}{2})+2$
or, $=1-\dfrac{3 \sqrt 3}{2}+2$
or, $=3-\dfrac{3\sqrt 3}{2}$
