# What is the period of f(theta) = tan ( ( 5theta)/12 )- cos ( ( theta)/ 3 ) ?

$12 \pi$
Period of $\tan \left(\frac{5 \pi}{12}\right) - \to \frac{12 \pi}{5}$
Period of $\cos \left(\frac{\pi}{3}\right)$ --> $3 \left(2 \pi\right) = 6 \pi$
Least common multiple of $\frac{12 \pi}{5}$ ans $6 \pi$ --> $12 \pi$
Period of f(t) --> $12 \pi$