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

[bubblygum]

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

 

[danago]

Consider using the Pythagorean identity on what you have come up with so far.

 

[bubblygum]

Great, solved it thanks.
Is the second one even possible?

 

[Bohrok]

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.