Sum and Difference Formulas PROVE

[ryno16]

Homework Statement

Given this formula

Sum
sin(a+b)=sin(a)*cos(b)+cos(a)*sin(b)

prove this one
Difference
sin(a-b)=sin(a)*cos(b)-cos(a)*sin(b)

Given this formula

Sum
cos(a+b)=cos(a)*cos(b)-sin(a)*sin(b)

prove this one
Difference
cos(a-b)=cos(a)*cos(b)+sin(a)*sin(b)

Homework Equations

(difference and sum equations stated in the problem)

The Attempt at a Solution

I assume it's the same concept for both of them, i just don't know how to go about proving it to be true.

 

[Mark44]

a - b = a + (-b), so sin(a - b) = ?

 

[SrEstroncio]

Like Mark44 said, use the fact that A - B = A + (-B).
Hint: Sine is an odd function, which means that f(-x) = -f(x)
2nd hint: Cosine is an even function, which means that f(-x) = f(x)

That should do the trick.