Q36 / 90 · KVPY 2012 (SB/SX) · Mathematics
The value of $\tan 81^{\circ}-\tan 63^{\circ}-\tan 27^{\circ}+\tan 9^{\circ}$ is $-$
- A0
- B2
- C3
- Correct answerD4
Solution
$\tan 81^{\circ}-\tan 63^{\circ}-\tan 27^{\circ}+\tan 9^{\circ}$
$\tan \left(90^{\circ}-9^{\circ}\right)-\tan \left(90^{\circ}-27^{\circ}\right)-\tan 27^{\circ}+\tan 9^{\circ}$
$\cot 9^{\circ}-\cot 27^{\circ}-\tan 27^{\circ}+\tan 9^{\circ}$
By solving we get
$=4$
Hence, the correct answer is option: 'D'.