Question

Sa se arate ca : sin(60°-x)-√3 sin (30°-x)=sin x

Answer 1

sin(60°-x)-√3 sin (30°-x)=
=sin60°cos x - sin x cos 60°-√3( sin 30°cos x -sin x cos 30°)=
=sin60°cos x - sin x cos 60°-√3 sin 30°cos x +√3 sin x cos 30°=
=√3/2 ×cos x - sin x ×1/2-√3×1/2 cos x +√3×√3/2 sin x =
=√3/2 ×cos x - (sin x )/2-√3/2 × cos x +3/2 sin x =
= sin x (-1/2 +3/2 ) = sin x