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## pottersheep 3 years ago 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)

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1. pottersheep

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

2. zordoloom

I can help.

3. pottersheep

Thank you so much

4. pottersheep

We have only learnt compound angles, by the way

5. zordoloom

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

6. pottersheep

I think so

7. zordoloom

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

8. pottersheep

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

9. zordoloom

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

10. zordoloom
11. pottersheep

Thanks Ill read it!

12. pottersheep

nope....never learnt those :s

13. zordoloom

Okay.

14. zordoloom

Give me like 5-10 minutes. This one is a little tricky. I'll try to keep you updated with the steps.

15. pottersheep

Alright I really appreciate it

16. pottersheep

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

17. pottersheep

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

18. pottersheep

ignore the caps they are the same letter

19. pottersheep

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

20. zordoloom

still working....

21. zordoloom

Okay, Do you know the double angle formula?

22. pottersheep

yep!

23. zordoloom

good.

24. zordoloom

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

25. zordoloom

Are you following what i mean here?

26. pottersheep

hmm

27. zordoloom

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

28. pottersheep

alright

29. zordoloom

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

30. pottersheep

yep

31. zordoloom

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

32. pottersheep

yep

33. zordoloom

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

34. pottersheep

one sec for the original question?

35. zordoloom

yes.

36. pottersheep

oh no! you are right it sin(x-y)!!!!!!!

37. pottersheep

sorry ><

38. zordoloom

Ok, that makes more sense now.

39. zordoloom

Give me another minute to type this up.

40. pottersheep

Of course

41. zordoloom

ok, i've got it.

42. pottersheep

:D

43. zordoloom

44. zordoloom

ok let me know if you can see it.

45. pottersheep

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

46. zordoloom

Yep.

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