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

The Correct Option is 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 $