Simplify:

sin(x-y)cosy+cos(x-y)siny
= (sinxcosy-cosxsiny)cosy+(cosxcosy+sinxsiny)siny
= ???

What do I do next???

Please Help and Thank You

expand it again

= sinx cos^2 y - cosxsinycosy + cosxcosysiny + sinxsin^2 y
= sinx(cos^2 y - sin^2 y)
= sinxcos(2y)

when I substitue the x's and y's I get different answers.

do I need brackets on (sinxcosy-cosxsiny) and (cosxcosy+sinxsiny)?

could the next step be: sinxcosy-cosxsinycosy+cosxcosy+sinxsinysiny without the brackets? or would that be wrong?

found my error

2nd last line should have been

= sinx(cos^2 y + sin^2 y)
= sinx (1)
= sinx

thank you so much=)

To simplify the expression: sin(x-y)cosy+cos(x-y)siny, we can start by expanding the trigonometric functions using the trigonometric identities:

sin(x-y) = sinxcosy - cosxsiny
cos(x-y) = cosxcosy + sinxsiny

Substituting these values into the expression, we get:

(sinxcosy-cosxsiny)cosy + (cosxcosy+sinxsiny)siny

Now, let's distribute the factors:

sinxcosycosy - cosxsiny*cosy + cosxcosysiny + sinxsinysiny

Next, simplify by multiplying the trigonometric functions:

sinxcosycosy - cosxsiny*cosy + cosxcosysiny + sinxsinysiny

Finally, combine like terms:

sinxcosycosy + cosxcosysiny - cosxsiny*cosy + sinxsinysiny

And this is the simplified form of the given expression.