Question

Expand the following
Sin(a+b-c)

Answer 1

We may remember,

sin(x + y) = sin(x) cos(y) + cos(x) sin(y)

sin(x - y) = sin(x) cos(y) - cos(x) sin(y)

cos(x + y) = cos(x) cos(y) - sin(x) sin(y)

Here, let  a + b = x.

    sin(a + b - c)

⇒  sin(x - c)

⇒  sin(x) cos(c) - cos(x) sin(c)

Taking  x  as  a + b,

⇒  sin(a + b) cos(c) - cos(a + b) sin(c)

⇒  [sin(a) cos(b) + cos(a) sin(b)] cos(c) - [cos(a) cos(b) - sin(a) sin(b)] sin(c)

⇒  sin(a) cos(b) cos(c) + cos(a) sin(b) cos(c) - cos(a) cos(b) sin(c) + sin(a) sin(b) sin(c)

Hence expanded!