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

Answer 1

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.