Докажите тождество sin(π/6+a)-cosa-cos(a-2π/3)=0

Question

Докажите тождество
sin(π/6+a)-cosa-cos(a-2π/3)=0

Answer 1

sin(π/6+a)-cosa-cos(a-2π/3)=0

sin(π/6+a)-cosa-cos(a-2π/3)=
=sin(π/6)cos(a)+sin(a)cos(π/6)-cosa-cos(a)cos(2π/3)-sin(a)sin(2π/3)=

=1/2cos(a)+sin(a)·(√3/2) - cosa - cos(a)·(-1/2)-sin(a)·(√3/2)=0