Докажите тождество 1) (cosa-cosb)^2 + (sina-sinb)^2=4sin^2 a-b/2 !

Cos²a-2cosacosb+cos²b+sin²a-2sinasinb+sin²b

=2-2(cosacosb+sinasinb)=

2-2cos(a-b)=2-2(cos²(a-b)/2-sin²(a-b)/2)=

2(cos²(a-b)/2+sin²(a-b)/2)-2cos²(a-b)/2+

2sin²(a-b)/2=4sin²(a-b)/2