Question

What is the period of `f(theta) = tan ( ( 8 theta)/9)- sec ( ( 7theta)/ 6)`?

Answer 1

`108pi`

Explanation:

Period of `tan ((8t)/9) --> (9pi)/8`
Period of `sec ((7t)/6) --> (12pi)/7`
Find least common multiple of `(9pi)/8 and (12pi)/7`

`(9pi)/8 ... X ... (8).(12) ... --> 108 pi`
`(12pi)/7 ... X ... (7).(9) ... --> 108pi`

Period of f(t) --> `108pi`