Question

The numbers of values of x in the interval (0,2pi) where f(x)=tan2x/tanx is undefined are:

Answer 1

Answer:

x=0,π,and2π. Explanation: Call tan x = t and apply the trig identity: tan2x= 2t1−t2. We get: 2t1−t2−t=2t−t+t31−t2=0.

Step-by-step explanation:

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Answer 2

Given : function is,

$f(x)=\frac{\tan 2x}{\tan x}$

To find : the number of values x takes in $(0, 2\pi)$.

Step-by-step explanation:

To get the values of x we have to do,

$f(x)=0\implies \frac{\tan 2x}{\tan x}=0\implies \tan 2x=0\implies 2x=n\pi$

$\therefore 2x=n\pi\implies x=\frac{n\pi}{2}$

Thus x will takes values $\{\frac{n\pi}{2} : 0<\frac{n\pi}{2}<2\pi\}$.