Question

What is the period of `f(theta) = tan ( ( 12 theta)/7 )- sec ( ( 14 theta)/ 6 )`?

Answer 1

`42pi`

Explanation:

Period of tan ((12t)/7) --> `(7pi)/12`
Period of `sec ((14t)/6) --> ((6)(2pi))/14 = (6pi)/7`
Period of f(t) is least common multiple of (7pi)/12 and (6pi)/7.

`(6pi)/7`........ x (7)(7) .... --> `42pi`
`(7pi)/12` ...... x (12)(6) .... --> `42pi`