Question

What is the period of `f(theta) = tan ( ( 12 theta)/7 )- sec ( ( 3 theta)/ 8 )`?

Answer 1

`(112pi)/3`

Explanation:

Period of `tan ((12t)/7) --> (7pi)/12`
Period of `sec ((3t)/8)` --> (16pi)/3
Period of f(t) --> least common multiple of `(7pi)/12 and (16pi)/3`

`(7pi)/12` ....x ( 64) ...--> `(448pi)/12 = (112pi)/3`
`(16pi)/3` ...x (7) ...--> `(112pi)/3`

Period of f(t) --> `(112pi)/3`