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Another problem

  • Thread starter Geekchick
  • Start date
  • #1
74
0

Homework Statement



sin5xcos3x=sin4xcos4x+sinxcosx, solve the identity

Homework Equations



all the identities and formulas mentioned in my last thread.

The Attempt at a Solution



Alright so I thought I could use the product to sum formula on the left side which ended up being 1/2sin10x then I used the sum/difference formula on the right side and got sin5x. Now according to my calculator these are not the same, so where have I gone wrong?
 

Answers and Replies

  • #2
Defennder
Homework Helper
2,591
5
Applying the product to sum formula to the left side is correct. But you don't end up with sin(10x). Where did you get that from?
 
  • #3
74
0
alright what i did was this.

original problem sin5xcos3x=sin4xcos4x+sinxcosx

Left side sin5xcos3x

Product to sum formula sinxcosx=1/2[sin(x+y)+sin(x-y)]
plug in the numbers

1/2[sin(5x+3x)+sin(5x-3x)]
simplify
1/2(sin8x+sin2x)
simplify
1/2sin10x

right side sin4xcos4x+sinxcosx

sum/difference formula sin(x+y) = sinxcosy + cosxsiny
plug in the numbers
oh,never mind that wont work its in the form sinxcosx +sinycosy hmmm.
 
  • #4
dynamicsolo
Homework Helper
1,648
4
You're more than halfway home. You have on the left side

1/2[sin(5x+3x)+sin(5x-3x)]
simplify
1/2(sin8x+sin2x)
This is fine. You can leave the left side now.

1/2(sin8x+sin2x)
simplify
1/2sin10x
Alas, angles don't add this way...

right side sin4xcos4x+sinxcosx
Here, don't apply the product-sum identity to the second term (well, you could, but it's overly fussy). What is sin x·cos x equal to (using another identity)? That will get you one of the pieces you're after.

Do use the product-sum identity to the first term -- now you'll be done...
 
  • #5
74
0
Thank you so much!
 

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