cos^2(a)+cos^2(60-a)+cos^2(60+a)
=cos^2(a)+[1/2*cos(a)+√3/2*sin(a)]^2+[1/2*cos(a)-√3/2*sin(a)]^2
=cos^2(a)+[1/4*cos^2(a)+3/4*sin^2(a)]*2
=3/2*cos^2(a)+3/2*sin^2(a)
=3/2
cos^2(a)+cos^2(60-a)+cos^2(60+a)
=cos^2(a)+[1/2*cos(a)+√3/2*sin(a)]^2+[1/2*cos(a)-√3/2*sin(a)]^2
=cos^2(a)+[1/4*cos^2(a)+3/4*sin^2(a)]*2
=3/2*cos^2(a)+3/2*sin^2(a)
=3/2