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

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(i) The value of tan A is always less than 1.  (ii) sec A = 12/5 for some value of angle A.  (iii) cos A is the abbreviation used for the cosecant of

Solution:

(i) The value of tan A is always less than 1.
Answer: False, because tan 45° = 1.

(ii) sec A = 12/5 for some value of angle A. 
Answer: False, because sec A ≠ 12/5 for any value of A.

(iii) cos A is the abbreviation used for the cosecant of angle A.
Answer: True.

(iv) cot A is the product of cot and A. 
Answer: False.

(v) sin θ = 4/3 for some angle θ.
Answer: False, because  sin θ ≠ 4/3 for any value of θ.
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