Evaluate the following:$ \frac{\tan 10^{\circ}}{\cot 80^{\circ}} $

Given:

\( \frac{\tan 10^{\circ}}{\cot 80^{\circ}} \)

To do:

We have to evaluate \( \frac{\tan 10^{\circ}}{\cot 80^{\circ}} \).

Solution:  

We know that,

$cot\ (90^{\circ}- \theta) = tan\ \theta$

Therefore,

$\frac{\tan 10^{\circ}}{\cot 80^{\circ}}=\frac{\tan 10^{\circ}}{\cot (90^{\circ}-10^{\circ})}$

$=\frac{\tan 10^{\circ}}{\tan 10^{\circ}}$

$=1$

Therefore, $\frac{\tan 10^{\circ}}{\cot 80^{\circ}}=1$.  

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Updated on: 10-Oct-2022

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