Q11. State whether the following are true or false. Justify your answer.

(i) The value of tan A is always less than 1.

(ii) \( secA \ = \ \frac{12}{5} \) for some value of angle A .

(iii) \(cos A \) is the abbreviation used for the cosecant of angle A.

(iv) \(cot A\) is the product of cot and A.

(v) \( sin\theta \ = \ \frac{4}{3} \) for some angle \( \theta \).

(i) The value of tan A is always less than 1.

(ii) \( secA \ = \ \frac{12}{5} \) for some value of angle A .

(iii) \(cos A \) is the abbreviation used for the cosecant of angle A.

(iv) \(cot A\) is the product of cot and A.

(v) \( sin\theta \ = \ \frac{4}{3} \) for some angle \( \theta \).

(i) False because sides of a right triangle may have any length, so tan A may have any value.

(ii) True as sec A is always greater than 1.

As, \( sec A \ = \ \frac{H}{B} \) and Hypotenuse is the largest side ∴ sec A is always greater than 1

(iii) False as cos A is the abbreviation used for cosine A.

(iv) False as cot A is not the product of 'cot' and A. 'cot' separated from A has no meaning.

(v) False as sin \( \theta \) cannot be > 1