Question

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

Answer 1

`84pi`

Explanation:

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

`(7pi)/12` ......x...(12)(12) .... --> `84pi`
`(12pi)/7`.......x......(7)(7) ..... --> `84pi`

Period of f(t) is `84pi`