Question

The value of $\tan 10^{\circ }\tan 20^{\circ }\tan 30^{\circ }\tan 40^{\circ }\tan 50^{\circ }\tan 60^{\circ }\tan 70^{\circ }\tan 80^{\circ }=$

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

Answer 1

Answer: (D)

$\tan 10^{\circ }\tan 20^{\circ }\tan 30^{\circ }\tan 40^{\circ }\tan 50^{\circ }\tan 60^{\circ }\tan 70^{\circ }\tan 80^{\circ }$
$=\tan (90-80{)}^{\circ }\tan (90-70{)}^{\circ }\tan (90-60{)}^{\circ }\tan (90-50{)}^{\circ }\tan 50^{\circ }\tan 60^{\circ }\tan 70^{\circ }\tan 80^{\circ }$
$=\tan 80^{\circ }\times \cot 80^{\circ }\times \tan 70^{\circ }\times \cot 70^{\circ }\times \tan 60^{\circ }\times \cot 60^{\circ }\times \tan 50^{\circ }\times \cot 50^{\circ }=1$