Solveeit Logo
Login

Question

Mathematics Question on Trigonometric Functions

The value of tan⁡10∘ tan⁡20∘ tan⁡30∘ tan⁡40∘ tan⁡50∘ tan⁡60∘tan⁡70∘ tan⁡80∘=\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

13 \frac{1}{\sqrt{3}}

D

1

Answer

1

Explanation

Solution

tan⁡10∘ tan⁡20∘ tan⁡30∘ tan⁡40∘ tan⁡50∘ tan⁡60∘tan⁡70∘ tan⁡80∘\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)∘tan⁡(90−70)∘tan⁡(90−60)∘tan⁡(90−50)∘tan⁡50∘tan⁡60∘tan⁡70∘tan⁡80∘= \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∘×cot⁡80∘×tan⁡70∘×cot⁡70∘×tan⁡60∘×cot⁡60∘×tan⁡50∘×cot⁡50∘=1= \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