State whether the following are true or false. Justify your answer.
The value of tan $ A $ is always less than 1 .
Given:
Given statement is:
The value of tan \( A \) is always less than 1.
To do:
We have to state whether the given statement is true or false.
Solution:
$\tan\ A =\frac{side\ opposite\ to\ A}{side\ adjacent\ to\ A}$
$=\frac{BC}{AB}$
In a triangle ABC, $BC$ can be greater than $AB$.
Therefore,
$\frac{BC}{AB}$ can be greater than 1.
This implies the value of $tan\ A$ can be greater than 1.
The given statement is false.
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