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

Period of $\tan \left(\frac{15 t}{4}\right)$ -->$\frac{4 \pi}{15}$
Period of $\cos \left(\frac{4 t}{5}\right)$ --> $\frac{10 \pi}{4} = \frac{5 \pi}{2}$
Find least common multiple of $\frac{4 \pi}{15} \mathmr{and} \frac{5 \pi}{2}$
$\frac{4 \pi}{15}$....X ...(5)(15) --> $20 \pi$
$\frac{5 \pi}{2} \ldots X \ldots \left(2\right) \left(4\right) \ldots - \to$20pi#
Period of f(t) --> $20 \pi$