Write 'True' or 'False' and justify your answer in each of the following:
$ \frac{\tan 47^{\circ}}{\cot 43^{\circ}}=1 $

Given:

\( \frac{\tan 47^{\circ}}{\cot 43^{\circ}}=1 \)

To do:

We have to find whether the given statement is true or false.

Solution:

We know that,

$\tan (90^o-\theta)=\cot \theta$

Therefore,

$\frac{\tan 47^{\circ}}{\cot 43^{\circ}}=\frac{\tan(90^{\circ}-43^{\circ})}{\cot 43^{\circ}}$

$=\frac{\cot 43^{\circ}}{\cot 43^{\circ}}$

$=1$

The given statement is true.

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Updated on: 10-Oct-2022

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