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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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