Thread: Sum and Difference Formulas PROVE

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)


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.

My guess is that you're supposed to let sin(a - b) = sin(a + (-b)), and then use the fact that sin(-x) = -sin(x).

Originally Posted by stapel

My guess is that you're supposed to let sin(a - b) = sin(a + (-b)), and then use the fact that sin(-x) = -sin(x).

Hmm, could you elaborate?

EDIT: solved, thank you for the hint

No longer necessary.

given that,
sin(a+b)=sin(a)*cos(b)+cos(a)*sin(b)

prove
sin(a-b)
= sin(a+(-b))
= sin(a)*cos(-b)+cos(a)*sin(-b)
__________________________
cos(-b)= cos (b),
sin(-b)= -sin (b).
------------------------------
= sin(a)*cos(b)-cos(a)*sin(b)

Originally Posted by pencil09

given that,
sin(a+b)=sin(a)*cos(b)+cos(a)*sin(b)

prove
sin(a-b)
= sin(a+(-b))
= sin(a)*cos(-b)+cos(a)*sin(-b)
__________________________
cos(-b)= cos (b),
sin(-b)= -sin (b).
------------------------------
= sin(a)*cos(b)-cos(a)*sin(b)

Then for solving/proving the second equation, how would i go about performing that? In the same manner?