Đáp án + Giải thích các bước giải:

$\begin{array}{l} \textbf{VT} &= \tan 9^\circ - \tan 27^\circ - \tan 63^\circ + \tan 81^\circ
\\ &= \tan 9^\circ - \tan 27^\circ - \tan (90^\circ - 27^\circ) + \tan (90^\circ - 9^\circ)
\\ &= \tan 9^\circ + \cot 9^\circ - (\tan 27^\circ + \cot 27^\circ)
\\ &= \dfrac{\sin 9^\circ}{\cos 9^\circ} +\dfrac{\cos 9^\circ}{\sin 9^\circ} - \bigg(\dfrac{\sin 27^\circ}{\cos 27^\circ} + \dfrac{\cos 27^\circ}{\sin 27^\circ}\bigg)
\\ &= \dfrac{\sin^2 9^\circ + \cos^2 9^\circ}{\sin 9^\circ \cos 9^\circ} - \dfrac{\sin^2 27^\circ + \cos^2 27^\circ}{\sin 27^\circ \cos 27^\circ}
\\ &=\dfrac{1}{\sin 9^\circ \cos 9^\circ} - \dfrac{1}{\sin 27\circ \cos 27^\circ}
\\ &= \dfrac{2}{2 \sin 9^\circ \cos 9^\circ} - \dfrac{2}{2 \sin 27^\circ \cos 27^\circ}
\\ &= \dfrac{2}{\sin 18^\circ} - \dfrac{2}{\sin 54^\circ}
\\ &= \dfrac{2(\sin 54^\circ - \sin 18^\circ)}{\sin 18^\circ \sin 54^\circ}
\\ &= \dfrac{2\big(2\cos \frac{54^\circ + 18^\circ}{2} \sin \frac{54^\circ - 18^\circ}{2}\big)}{\sin 18^\circ \sin 54^\circ}
\\ &= \dfrac{4 \cos 36^\circ \sin 18^\circ}{\sin 18^\circ \cos 36^\circ}
\\ &= 4= \textbf{VP} \end {array}$