Question

What is the period of `f(theta) = tan ( (15 theta)/4 )- cos ( (4 theta)/ 5 )`?

Answer 1

Period of `tan ((15t)/4)` -->`(4pi)/15`
Period of `cos ((4t)/5)` --> `(10pi)/4= (5pi)/2`
Find least common multiple of `(4pi)/15 and (5pi)/2`

`(4pi)/15`....X ...(5)(15) --> `20pi`
`(5pi)/2 ... X ... (2)(4) ... -->`20pi#

Period of f(t) --> `20pi`