<s>[INST] Find the value of $\displaystyle\sqrt{3} \cdot \cot (20^{\circ}) - 4 \cdot \cos (20^{\circ}) $ How to find the value of
$$\displaystyle\sqrt{3} \cdot \cot (20^{\circ}) - 4 \cdot \cos (20^{\circ})$$
manually ?
 [/INST] Like Trigonometry Simplification,
$$\frac{2\sin60^\circ\cdot\cos20^\circ-2(2\sin20^\circ\cos20^\circ)}{\sin20^\circ}$$
Using Werner Formula we get,
$$\frac{\sin80^\circ+\sin40^\circ-2\sin40^\circ}{\sin20^\circ}$$
Using Prosthaphaeresis Formula,  $\sin80^\circ-\sin40^\circ=2\sin20^\circ\cos60^\circ$
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