If $n \in N$ and the period of $\frac{\cos(nx)}{\sin(x/n)}$ is $4\pi$,then $n$ is equal to

If the period of the function $f(x) = \frac{\tan 5x \cos 3x}{\sin 6x}$ is $\alpha$,then find the value of $f\left(\frac{\alpha}{8}\right)$.

Let $f(x) = \sin^2 x + \cos^4 x + 2$ and $g(x) = \cos(\cos x) + \cos(\sin x)$. Also,let the period of $f(x)$ and $g(x)$ be $T_1$ and $T_2$ respectively,then:

Let $f(x) = \cos(ax) + \sin(x)$ be a periodic function. Then $a$ must be

If $f: R \rightarrow R$ is defined by $f(x) = 7 + \cos(5x + 3)$ for $x \in R$,then the period of $f$ is

The function $f(x) = \sin \frac{\pi x}{2} + 2\cos \frac{\pi x}{3} - \tan \frac{\pi x}{4}$ is periodic with period