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# Non-permissible values of x

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Can't figure out all of the non-permissible values of (cot(x))/(2sin^2(x)-1).

So far I've got 0, 1 and pi +npi (n being any integer) but I'm not even sure if those are right. Any help would be much appreciated.

Jan 16, 2018

### 2+0 Answers

#1
+103701
+2

Can't figure out all of the non-permissible values of (cot(x))/(2sin^2(x)-1).

So far I've got 0, 1 and pi +npi (n being any integer) but I'm not even sure if those are right. Any help would be much appreciated.
$$Cot x = \frac{cos(x)}{sin(x)}\\ \text{So it is not defined when sin(x)=0}\\\text{ which is when x is any integer multiple of }\pi\\~\\ \text{So the non permissable values of x will include }\\ x=n\pi\qquad \text{Where n is any integer}$$

ALSO

The deominator cannot equal 0 so

$$2sin^2x-1\ne0\\ sin^2x\ne \frac{1}{2}\\ sinx\ne \pm\frac{1}{\sqrt2}\\ x\ne \frac{\pi}{4}+\frac{n\pi}{2}\\ x\ne \frac{\pi}{4}(1+2n)\qquad n\in Z$$

so the non-permsissable values are

$$x = n\pi\qquad and \qquad x= \frac{\pi}{4}(2n+1)\qquad n\in Z$$

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I have written this in LaTex which I think other people will be able to properly but it will not display properly for me.

Once I hit the preview button it will only show the raw code. When I hit post it will still only show the raw code.

Yes as I expected.

Jan 16, 2018
#2
+119
+2

Thanks!!! It finally makes sense to me.

Aleguan  Jan 16, 2018