Question

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

• A. $0$
• B. Not defined
• C. $1$
• D. $-1$

Answer 1

Answer: (C)

$1$

Using,

$\tan x=\cot ({90}^{\circ }-x)$ and $\tan x.\cot x=1$

We get ,

$\tan 5.\tan 10.\tan \mathrm{15...}\tan 80.\tan 85=\tan 5.\tan 10.\tan \mathrm{15...}\tan 45.\cot (90-35)...\cot (90-10).\cot (90-5)=\tan 5.\cot 5.\tan 10.\cot \mathrm{10...}\tan 45=1$