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Question
State whether the following are true or false. Justify your answer.
The value of tan A is always less than 1.
Options
True
False
Solution
This statement is False.
Explanation:
Consider a ΔABC, right-angled at B.
tan A = `("Side opposite to ∠A")/("Side adjacent to ∠A")`
= `12/5`
But `12/5 > 1`
∴ tan A > 1
So, tan A < 1 is not always true.
Hence, the given statement is false.
A tangent of an angle is the ratio of sides other than hypotenuse, which may be equal or unequal to each other.
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