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

sec A = 12/5 for some value of angle A.

Dear Student
the answer is:
True

Justification: Let a ΔMNC in which∠N = 90 degrees.
MC=12k and MB=5k, where k is a positive real number.
By Pythagoras theorem we get,
MC^2=MN^2+NC^2
(12k)^2=(5k)^2+NC^2
NC^2+25k^2=144k^2
NC^2=119k^2
Such a triangle is possible as it will follow the Pythagoras theorem.

Thanks