Question

$\tan 9^{\circ }\times \tan {27}^{\circ }\times \tan {63}^{\circ }\times \tan {81}^{\circ }$ is equal to

• A. $4$
• B. $3$
• C. $2$
• D. $1$

Answer 1

The correct option is D $1$

$\tan 9°\times \tan 27°\times \tan 63°\times \tan 81°$

$=\tan (90°-81°)\times \tan (90°-63°)\times \tan 63°\times \tan 81°$

$=\cot 81°\times \cot 63°\times \tan 63°\times \tan 81°$

$=1.$...............$\tan \theta =\frac{1}{\cot \theta }$

Hence, the answer is $1.$