Question

$\tan {10}^{\circ }\tan {20}^{\circ }\tan {30}^{\circ }\tan {40}^{\circ }\tan {50}^{\circ }\tan {60}^{\circ }\tan {70}^{\circ }\tan {80}^{\circ }$ is equal to

• A. $0$
• B. $-1$
• C. $\frac{1}{\sqrt{3}}$
• D. $1$

Answer 1

Answer: (D)

$1$

$\tan {10}^{\circ }\tan {20}^{\circ }\tan {30}^{\circ }\tan {40}^{\circ }\tan {50}^{\circ }\tan {60}^{\circ }\tan {70}^{\circ }\tan {80}^{\circ }$

we know that $\tan (90-\theta )=\cot \theta$

$=\tan {10}^{\circ }.\tan {20}^{\circ }.\tan {30}^{\circ }.\tan {40}^{\circ }.\cot {40}^{\circ }.\cot {30}^{\circ }.\cot {20}^{\circ }.\cot {10}^{\circ }$
$=1$...........Use $\tan ({90}^o-\theta )=\cot \theta$ and $\tan \theta \cot \theta =1$