Answer
$\dfrac{1}{2}$
Work Step by Step
We know the following trigonometric values:
$\sin 30^{\circ}=\dfrac{1}{2}$ and $\tan 45^{\circ}=1$
We can re-write as the angles as:
$\dfrac{\pi}{4}=45^{\circ}$ and $\dfrac{\pi}{6}=30^{\circ}$
Therefore,
$\tan \dfrac{\pi}{4} -\sin \dfrac{\pi}{6}=\tan 45^{\circ}-\sin 30^{\circ}$
Now, $\tan 45^{\circ}-\sin 30^{\circ}=1-\dfrac{1}{2}=\dfrac{1}{2}$
