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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) 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