Write 'True' or 'False' and justify your answer.
$\frac{\tan 47^{\circ}}{\cot 43^{\circ}}=1$
$\frac{\tan 47^{\circ}}{\cot 43^{\circ}}=1$
(TRUE) True
We know that $\tan(90^{\circ} - \theta) = \cot \theta$.
Therefore,$\tan 47^{\circ} = \tan(90^{\circ} - 43^{\circ}) = \cot 43^{\circ}$.
Substituting this into the expression:
$\frac{\tan 47^{\circ}}{\cot 43^{\circ}} = \frac{\cot 43^{\circ}}{\cot 43^{\circ}} = 1$.
Thus,the given statement is True.
We know that $\tan(90^{\circ} - \theta) = \cot \theta$.
Therefore,$\tan 47^{\circ} = \tan(90^{\circ} - 43^{\circ}) = \cot 43^{\circ}$.
Substituting this into the expression:
$\frac{\tan 47^{\circ}}{\cot 43^{\circ}} = \frac{\cot 43^{\circ}}{\cot 43^{\circ}} = 1$.
Thus,the given statement is True.
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