2011-01-11, 03:52 AM
sin(a+b) = sina cosb + cosa sinb
sin(a-b) = sina cosb - cosa sinb
cos(a+b) = cosa cosb - sina sinb
cos(a-b) = cosa cosb + sina sinb
Is there a way to prove these using calculus? (Using derivatives and integrals).
Their form looks a lot like the product rule (xy)' = xy'+x'y. If we take the first one, for example...
int (sina cosb + cosa sinb) = (sina)(cos b)
I'm not sure how to derive the above equation to make it look like sin(a+b).
sin(a-b) = sina cosb - cosa sinb
cos(a+b) = cosa cosb - sina sinb
cos(a-b) = cosa cosb + sina sinb
Is there a way to prove these using calculus? (Using derivatives and integrals).
Their form looks a lot like the product rule (xy)' = xy'+x'y. If we take the first one, for example...
int (sina cosb + cosa sinb) = (sina)(cos b)
I'm not sure how to derive the above equation to make it look like sin(a+b).