Question

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

Answer 1

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

Answer 2

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?

Answer 3

found my error
2nd last line should have been

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

Answer 4

thank you so much=)