How can I expand sin(x + y) + sin(x - y) to get 2sinxcosy?

AI Thread Summary
The discussion focuses on proving trigonometric identities, specifically expanding sin(x + y) + sin(x - y) to derive 2sinxcosy. Participants explore the right-hand side of the equation cos(x+y)cos(x-y) and attempt to simplify it, ultimately questioning whether their approach is correct. The left-hand side is successfully simplified using sine identities, confirming the identity holds true. Additionally, the conversation confirms that the second identity is indeed possible through proper expansion. The thread emphasizes the importance of using trigonometric identities for simplification in proving equations.
bubblygum
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Proving trig identities

I have 2 more this time, thanks for the time!

Homework Statement


-sin^2x-sin^2y+1=cos(x+y)cos(x-y)

Homework Equations


Compound, double, pythagorean, reciprocal, quaotient, etc.

The Attempt at a Solution


R.H.S.
cos(x+y)cos(x-y)
= (cosxcosy-sinxsiny)(cosxcosy+sinxsiny)
= cos^2xcos^2y - sin^2xsin^2y

Not sure how to finish this off. Or have I started it off wrong?

Homework Statement


sin(x+y)+sin(x-y)=2sinxcosx


Homework Equations


Same as above


The Attempt at a Solution


L.H.S.
sin(x+y)+sin(x-y)
= sinxcosy+sinycosx + sinxcosy-sinycosx
= sinxcosy+sinxcosy
= 2sinxcosy
 
Last edited:
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Consider using the Pythagorean identity on what you have come up with so far.
 
Great, solved it thanks.
Is the second one even possible?
 
bubblygum said:
Is the second one even possible?

Yes, just expand sin(x + y) + sin(x - y) using the sum and difference identities for sine and you'll get it.
 

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