Ask Questions, Get Answers

Want to ask us a question? Click here
Browse Questions
Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Trignometry
0 votes

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

Can you answer this question?

1 Answer

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

Related questions

Ask Question
student study plans
JEE MAIN, CBSE, AIPMT Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App