pottersheep
  • pottersheep
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
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
pottersheep
  • pottersheep
I've been at it for so long! I cant get it :(
anonymous
  • anonymous
I can help.
pottersheep
  • pottersheep
Thank you so much

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

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