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

Nov 9, 2016

$108 \pi$

#### Explanation:

Period of $\tan \left(\frac{8 t}{9}\right) - \to \frac{9 \pi}{8}$
Period of $\sec \left(\frac{7 t}{6}\right) - \to \frac{12 \pi}{7}$
Find least common multiple of $\frac{9 \pi}{8} \mathmr{and} \frac{12 \pi}{7}$

$\frac{9 \pi}{8} \ldots X \ldots \left(8\right) . \left(12\right) \ldots - \to 108 \pi$
$\frac{12 \pi}{7} \ldots X \ldots \left(7\right) . \left(9\right) \ldots - \to 108 \pi$

Period of f(t) --> $108 \pi$