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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Trignometry
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The value of $\tan 81^{\large \circ}-\tan 63^{\large\circ}-\tan 27^{\large\circ}+\tan 9^{\large \circ}$ is

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$\tan 81^{\large\circ}-\tan 63^{\large\circ}-\tan 27^{\large \circ}+\tan 9^{\large\circ}$
$\Rightarrow \tan 9^{\circ}+\cot 9^{\large \circ}-\tan 27^{\large \circ}-\cot 27^{\large\circ}$
$\Rightarrow \large\frac{1}{\sin 9^{\Large \circ}\cos 9^{\Large\circ}}-\frac{1}{\sin 27^{\Large \circ}\cos 27^{\Large\circ}}$
$\Rightarrow \large\frac{2}{\sin 18^{\large\circ}}- \large\frac{2}{\sin 54^{\large\circ}}$
$\Rightarrow \large\frac{2}{\sin 18^{\large\circ}}- \large\frac{2}{\cos 36^{\large\circ}}$
$\Rightarrow \large\frac{2\times 4}{\sqrt 5-1}-\frac{2\times 4}{\sqrt {5}+1}$
$\Rightarrow \large\frac{8[\sqrt 5+1-\sqrt 5+1]}{5-1}$
$\Rightarrow 8\big[\large\frac{2}{4}\big]$
$\Rightarrow 4$
Hence (d) is the correct option.
answered Oct 9, 2013 by sreemathi.v
 

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