solve

replace with

or

for is it correct to say there are no solutions for this?

for the other one I got

Are these all the solutions in the interval, or does cot2x =0 also have a solution?

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- Jan 21st 2010, 12:03 PMTweetytrig equation - all solutions
solve

replace with

or

for is it correct to say there are no solutions for this?

for the other one I got

Are these all the solutions in the interval, or does cot2x =0 also have a solution? - Jan 21st 2010, 12:26 PMbigwave
- Jan 21st 2010, 12:27 PMArchie Meade
The numerator of cot2x is cos2x.

This is zero for

- Jan 21st 2010, 12:48 PMTweety
- Jan 21st 2010, 12:57 PMbigwavecotx = cosx\sinx
- Jan 21st 2010, 01:00 PMTweety
- Jan 21st 2010, 01:02 PMArchie Meade
That one is the ratio for Tan2x, Tweety, ie

which is Tan2x inverted.

So the other two solutions are found by solving Cos2x=0,

since Cot2x=0 when the numerator Cos2x is zero. - Jan 21st 2010, 01:03 PMTweety
Actually I was just wondering,

I have

that would be the same as witting

...meaning tan2x couldn't = 0 ? So how come these other to solutions are 'valid'?

Can someone please explain, thanks. - Jan 21st 2010, 01:05 PMArchie Meade
You may be thinking of Tan2x going to infinity,

but yes it does when Cos2x goes to zero.

goes to zero when x goes to infinity. - Jan 21st 2010, 01:06 PMbigwave
- Jan 21st 2010, 01:10 PMTweety
Okay, I kind of 'get it' , thanks for your help.

- Jan 21st 2010, 01:23 PMArchie Meade

You can think it through with little fractions first.

since the numerator is twice the denominator.

To divide by a fraction, just turn it upside down and multiply instead.

Therefore

is Tan2x upside down.