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



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pottersheep
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I've been at it for so long! I cant get it :(

zordoloom
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I can help.

pottersheep
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Thank you so much

pottersheep
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We have only learnt compound angles, by the way

zordoloom
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So there is an identity that's called co function identies, do you know them?

pottersheep
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I think so

zordoloom
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Or sum to product identities. Do any of these sound familiar.

pottersheep
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Is it the cos(90x) kind of thing?

zordoloom
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um, not really. Here, let me post a link.


pottersheep
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Thanks Ill read it!

pottersheep
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nope....never learnt those :s

zordoloom
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Okay.

zordoloom
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Give me like 510 minutes. This one is a little tricky. I'll try to keep you updated with the steps.

pottersheep
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Alright I really appreciate it

pottersheep
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I found a note that our teacher wrote on the board! I dont get it though...
he wrote

pottersheep
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sinx + siny = sin(a+b) = sinacosB + cosAsinB
sin(ab) = sinAcosB  cosAsinB
sin(a+B) + sin (a  b) = 2sinAcosB

pottersheep
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ignore the caps they are the same letter

pottersheep
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Then he wrote : let : a+b = x
a  b = y
2a = x+y
x = (x+y)/2

zordoloom
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still working....

zordoloom
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Okay, Do you know the double angle formula?

pottersheep
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yep!

zordoloom
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good.

zordoloom
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okay, so cos([x+y]/2)sin([x+y]/2).
This equal sin(x+y)

zordoloom
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Are you following what i mean here?

pottersheep
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hmm

zordoloom
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how about this.
2cosAsinA=sin2a. A=(x+y)/2

pottersheep
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alright

zordoloom
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cosine of x is sine of (90x) right?

pottersheep
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yep

zordoloom
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okay. so
=sin(x+y)
=sinxcosy+sinycosx
=sinx sin(90y)+siny sin(90x)

pottersheep
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yep

zordoloom
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I have a quick question, is it sin(x+y)/2 or sin(xy)/2?

pottersheep
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one sec for the original question?

zordoloom
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yes.

pottersheep
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oh no! you are right it sin(xy)!!!!!!!

pottersheep
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sorry ><

zordoloom
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Ok, that makes more sense now.

zordoloom
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Give me another minute to type this up.

pottersheep
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Of course

zordoloom
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ok, i've got it.

pottersheep
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:D

zordoloom
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zordoloom
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ok let me know if you can see it.

pottersheep
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I can see it! Im following through fine so far. Thank you so much

zordoloom
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Yep.