Use of trig identities

[Albert Chan]

cos product to cos sum identity proof, using complex numbers.

cos(a)*cos(b)
= (cis(a)+cis(-a))/2 * (cis(b)+cis(-b))/2
= (cis(a+b)+cis(-(a+b))/4 + (cis(a-b)+cis(-(a-b))/4
= cos(a+b)/2 + cos(a-b)/2

Cas> simplify(exp2trig(trig2exp(cos(a)*cos(b))))

1/2*cos(a+b) + 1/2*cos(a-b)