Solve the equation tan^2xcscx=tan^2x on [0, 2π ).

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- anonymous

Solve the equation tan^2xcscx=tan^2x on [0, 2π ).

- schrodinger

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- anonymous

The equation written properly is: \[\tan^{2}xcscx=\tan^{2}x\]

- anonymous

Try rearranging the equation by bringing everything over to the left. Then factorise out tan^2(x). Then you will have a product. Equate both bits equal to zero and solve them. :)
I'm not sure that that is very clear, so let me know :)

- anonymous

well what I did was:
tan^2xcscx-tan^2x=0
and then i tried to factor out tanx
tanx(tanxcscx-tanx)
then i realized i should factor out tan^2x
tan^2x (cscx-1)
and i made those 2 seperate equations:
tan^2x=0 and cscx=1
with the cscx=1 i got pi/2
however i am unsure what to do with the tan^2x=0 because of the square

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- anonymous

@jamie133 have i done it correct so far?

- anonymous

I think pi/2 is correct!
And to get rid of the square, square root both sides. You can do this without worrying about getting a plus or minus, because it is equal to 0. There is no -0.

- anonymous

so it would be tanx=0 giving me 0 and pi.
i am not sure if this is correct because it is a multiple choice problem and the answers are:
A. x=0
B. x=0 or x=pi
C. x=pi/2 or 3pi/2
D. no solution
if i get 0, pi and pi/2 which would be the correct answer @jamie133

- anonymous

Hmmm, well it seems that you're working on a funny interval. Because on [0,2pi), tan(x) isn't always defined, and neither is cosec(x).
If you actually substitute in 0, pi or pi/2, then you should find that for each one, either tan(x) or cosec(x) is undefined.
So, I'm thinking that there are not any solutions for this!

- anonymous

you are correct! thank you!!

- anonymous

No problem :)
That was a close one, I hadn't noticed the interval!

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