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# Trigonometry question - I'm stuck! watch

Prove that:

cot 2x + cosec 2x = cot x

At first I thought it looked ok, but I seem to get stuck with cos at the end.... My brain isn't functioning today. (Maths exam on monday!!)

Thanks

Laura xxx
2. cot 2x = cos2x/sin2x

cosec 2x = 1/sin 2x

so: (cos 2x + 1)/sin2x as common denominator.

sin2x = 2sin x cos x

cos 2x = 2cos^2 x - 1

so: (2cos^2 x -1)/ (2sinxcosx)

2's cancel cos x cancels with cos^2 x to leave cosx/sinx which is cot x

3. cot 2x + cosec2x
= cos2x/sin2x + 1/sin2x
= (cos2x + 1)/sin2x
= 2cos²x/2sinxcosx
= cosx/sinx
= cotx
=====
4. I swear I replied to this thread a few minutes ago...

Edit:
I thought I was imagining things, but it turns out I actually did!
5. dvs - you did reply - I read it !!! - and now I get it.

Thanks, by the way, and thanks to the others too.

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