Evaluate the following:
$ \frac{\tan 35^{\circ}}{\cot 55^{\circ}}+\frac{\cot 78^{\circ}}{\tan 12^{\circ}}-1 $

Given:

\( \frac{\tan 35^{\circ}}{\cot 55^{\circ}}+\frac{\cot 78^{\circ}}{\tan 12^{\circ}}-1 \)

To do:

We have to evaluate \( \frac{\tan 35^{\circ}}{\cot 55^{\circ}}+\frac{\cot 78^{\circ}}{\tan 12^{\circ}}-1 \).

Solution:  

We know that,

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

Therefore,

$\frac{\tan 35^{\circ}}{\cot 55^{\circ}}+\frac{\cot 78^{\circ}}{\tan 12^{\circ}}-1=\frac{\tan 35^{\circ}}{\cot (90^{\circ}-35^{\circ})}+\frac{\cot (90^{\circ}-12^{\circ})}{\tan 12^{\circ}}-1$

$=\frac{\tan 35^{\circ}}{\tan 35^{\circ}}+\frac{\tan 12^{\circ}}{\tan 12^{\circ}}-1$

$=1+1-1$

$=1$

Therefore, $\frac{\tan 35^{\circ}}{\cot 55^{\circ}}+\frac{\cot 78^{\circ}}{\tan 12^{\circ}}-1=1$.   

Tutorialspoint

Updated on: 10-Oct-2022

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