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I really need help with this Trig identity please!(Grade 12!) How do I prove that sinx-siny = 2cos([x+y]/2)sin([x+y]/2)

Mathematics
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I've been at it for so long! I cant get it :(
I can help.
Thank you so much

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Other answers:

We have only learnt compound angles, by the way
So there is an identity that's called co function identies, do you know them?
I think so
Or sum to product identities. Do any of these sound familiar.
Is it the cos(90-x) kind of thing?
um, not really. Here, let me post a link.
http://www.sosmath.com/trig/Trig5/trig5/trig5.html
Thanks Ill read it!
nope....never learnt those :s
Okay.
Give me like 5-10 minutes. This one is a little tricky. I'll try to keep you updated with the steps.
Alright I really appreciate it
I found a note that our teacher wrote on the board! I dont get it though... he wrote
sinx + siny = sin(a+b) = sinacosB + cosAsinB sin(a-b) = sinAcosB - cosAsinB sin(a+B) + sin (a - b) = 2sinAcosB
ignore the caps they are the same letter
Then he wrote : let : a+b = x a - b = y 2a = x+y x = (x+y)/2
still working....
Okay, Do you know the double angle formula?
yep!
good.
okay, so cos([x+y]/2)sin([x+y]/2). This equal sin(x+y)
Are you following what i mean here?
hmm
how about this. 2cosAsinA=sin2a. A=(x+y)/2
alright
cosine of x is sine of (90-x) right?
yep
okay. so =sin(x+y) =sinxcosy+sinycosx =sinx sin(90-y)+siny sin(90-x)
yep
I have a quick question, is it sin(x+y)/2 or sin(x-y)/2?
one sec for the original question?
yes.
oh no! you are right it sin(x-y)!!!!!!!
sorry ><
Ok, that makes more sense now.
Give me another minute to type this up.
Of course
ok, i've got it.
:D
ok let me know if you can see it.
I can see it! Im following through fine so far. Thank you so much
Yep.

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