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

1.	State whether the following are true or false. Justify your answer. (i) The value of tan A is always less than (ii) sec A = \(\frac{12}{5}\) 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 \(\theta\) .
Answer» (i) The value of tan 90° is greater than 1. Therefore, given statement is false. (ii) sec A = \(\frac{12}{5}\) \(\implies\) cos A = \(\frac{5}{12}\) as 12 is the hypotenuse largest side. Therefore, given statement is true. (iii) cos A is the abbreviation used for cosine of angle A Therefore, given statement is true. (iv) cot A is not the product of cot and A. Therefore, given statement is false. (v) Since, the hypotenuse is the longest side whereas in sin A =\(\frac{4}{3}\) , 3 which is the denominator and cannot be hypotenous.

State whether the following are true or false. Justify your answer. (i) The value of tan A is always less than (ii) sec A = \(\frac{12}{5}\) 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 \(\theta\) .

Answer»

(i) The value of tan 90° is greater than 1. Therefore, given statement is false.

(ii) sec A = \(\frac{12}{5}\) \(\implies\) cos A = \(\frac{5}{12}\) as 12 is the hypotenuse largest side. Therefore, given statement is true.

(iii) cos A is the abbreviation used for cosine of angle A Therefore, given statement is true.

(iv) cot A is not the product of cot and A. Therefore, given statement is false.

(v) Since, the hypotenuse is the longest side whereas in sin A =\(\frac{4}{3}\) , 3 which is the denominator and cannot be hypotenous.