Решите уравнение: а) √3/2cos x-1/2 sin x=1 б)√3 cos x-sin x=1 докажите тождество: sin(30-a)-cos(60-a)=-√3sina

1)cosπ/6cosx-sinπ/6sinx=1
cos(x+π/6)=1
x+π/6=2πn
x=-π/6+2πn
2)2(√3/2cosx-1/2sinx)=1
2(cosπ/6cosx-sinπ/6sinx)=1
cos(x+π/6)=1/2
x+π/6=-π/3+2πn U x+π/6=π/3+2πn
x=-π/2+2πn U x=π/6+2πn
3)sin(30-a)-cos(60-a)=sin30cosa-cos30sina-cos60cosa-sin60sina=
=1/2cosa-√3/2sina-1/2cosa-√3/2sina=-√3sina
-√3sina=-√3sina