Question

$tan9-tan27-tan63+tan81=$

• A. $\frac{1}{2}$
• B. 2
• C. 4
• D. 8

Answer 1

The correct option is C 4

Let,

$x=\tan 81+\tan 9-(\tan 63+\tan 27)$

$=\cot 9+\tan 9-(\cot 27+\tan 27)$

$=\frac{(\cos 9{)}^2+(\sin 9{)}^2}{\sin 9\cdot \cos 9}-\frac{(\cos 27{)}^2+(\sin 27{)}^2}{\sin 27\cdot \cos 27}$

$=\frac{1}{\sin 9\cdot \cos 9}-\frac{1}{\sin 27\cdot \cos 27}$

$=\frac{2}{\sin 18}-\frac{2}{\sin 54}$

$=2\cdot \frac{\sin 54-\sin 18}{\sin 54\cdot \sin 18}$

$=\frac{4\cos 36\cdot \sin 18}{\cos 36\cdot \sin 18}$

$=4$