Sin a sin 2a-cos a cos 2a-sin 3a

Question

Sin a sin 2a-cos a cos 2a-sin 3a

Answer 1

(Sin a sin 2a-cos a cos 2a)-sin 3a=-( cos a cos 2a+ Sin a sin 2a)-sin3a=
=-cos3a-sin3a=-(cos3a+sin3a)=-(cos3a+cos(π/2-3a))=
-2cos(3a+π/2-3a)/2·cos(3a-π/2+3a)/2=-2cosπ/4·cos(3a-π/4)=
=-2·√2/2· cos(3a-π/4)=-√2 cos(3a-π/4)