Question

The value of $\tan 5^{\circ }\tan {10}^{\circ }\tan {15}^{\circ }\tan {20}^{\circ }.......\tan {85}^{\circ }$ is

• A. 1
• B. 2
• C. 3
• D. none of these

Answer 1

The correct option is A 1

By looking at sequence you will observe that you have pair of $tan\theta andcot\theta$ and $tan\theta .cot\theta =1$
$tan{85}^{\circ }=tan(90-5)=cot{5}^{\circ }$ and $tan{5}^{\circ }.cot{5}^{\circ }=1$ find all these type of pairs and find the value