# The value of $\tan 81^{\large \circ}-\tan 63^{\large\circ}-\tan 27^{\large\circ}+\tan 9^{\large \circ}$ is

$(a)\;1\qquad(b)\;2\qquad(c)\;3\qquad(d)\;4$

$\tan 81^{\large\circ}-\tan 63^{\large\circ}-\tan 27^{\large \circ}+\tan 9^{\large\circ}$
$\Rightarrow \tan 9^{\circ}+\cot 9^{\large \circ}-\tan 27^{\large \circ}-\cot 27^{\large\circ}$
$\Rightarrow \large\frac{1}{\sin 9^{\Large \circ}\cos 9^{\Large\circ}}-\frac{1}{\sin 27^{\Large \circ}\cos 27^{\Large\circ}}$
$\Rightarrow \large\frac{2}{\sin 18^{\large\circ}}- \large\frac{2}{\sin 54^{\large\circ}}$
$\Rightarrow \large\frac{2}{\sin 18^{\large\circ}}- \large\frac{2}{\cos 36^{\large\circ}}$
$\Rightarrow \large\frac{2\times 4}{\sqrt 5-1}-\frac{2\times 4}{\sqrt {5}+1}$
$\Rightarrow \large\frac{8[\sqrt 5+1-\sqrt 5+1]}{5-1}$
$\Rightarrow 8\big[\large\frac{2}{4}\big]$
$\Rightarrow 4$
Hence (d) is the correct option.