Question

$z_{1} =(cos \alpha - cos \beta ) ^{2} - (sin \alpha - sin \beta ) ^{2}$

Answer 1

z1 = cos^2(a) - 2cosacosb + cos^2(b) - (sin^2(a) - 2sinasinb + sin^2(b)) = cos(2a) + cos(2b) - 2cosacosb - 2sinasinb = cos(2a) + cos(2b) - 2*cos(a-b)

z1 = cos(2a) + cos(2b) - 2*cos(a-b)