Question

the period of cot x/4+tan x/4/1+tan x/2-tan x is​

Answer 1

Answer:

I wanted to answer but unable to do so.

Answer 2

Answer:

$4\pi$

Step-by-step explanation:

Let's take a function  $f(x) = \frac{h(x)}{g(x)}$

If period of $h(x)$ is a, and period of $g(x)$ is b, then period of $f(x)$ is LCM(a,b)

Also, if $f(x) = g(x) + h(x)$ and if period of  $g(x)$  is a and period of $h(x)$ is b, then period of $f(x)$ is again LCM(a,b)

Period of tan(kx) and cot(kx) is $\frac{\pi }{|k|}$

So here the function is

$f(x) = \frac{cot(\frac{x}{4} )+tan(\frac{x}{4} )}{1+tan(\frac{x}{2} )-tan(x)}$

$h(x) = cot(\frac{x}{4} )+tan(\frac{x}{4} )}$

$g(x) = 1 + tan(\frac{x}{2} )-tan(x)$

Lets calculate period for $h(x)$ and  $g(x)$ now

Period of  $h(x)$ = LCM ( $4\pi$, $4\pi$) = $4\pi$

Period of  $g(x)$ = LCM ( 1, $2\pi$, $\pi$) = $2\pi$

Hence, period of $f(x)$ is LCM ( $2\pi$, $4\pi$ ) which is $4\pi$