Question

How do you simplify `sin(a-270)cos(-a) + cos(a-270)sin(-a)`?

Answer 1

Use the following identities:

•`sin(A - B) = sinAcosB - cosAsinB`

•`cos(A - B) = cosAsinB + sinAsinB`

•`sin(-x) = -sinx`

•`cos(-x) = cosx`

•`cos^2theta + sin^2theta = 1`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`=(sinacos270˚ - cosasin270˚)(cosa) + (cosacos(270˚) + sinasin(270˚))(-sina)`

`=(sina(0) - cosa(-1))(cosa) + (cosa(0) + sina(-1))(-sina)`

`=cos^2a + (-sina)(-sina)`

`=cos^2a + sin^2a`

`=1`

Hopefully this helps!