Упростите 2 cos 10°cos40° - cos50°

Question

Упростите 2 cos 10°cos40° - cos50°

Answer 1

Cos10cos40=1/2(cos(10-40)+cos(10+40))=1/2(cos(-30)+cos50)=*
cos(-30)=cos(30) -четная
*=1/2(cos30+cos50)
2*1/2(cos30+cos50)-cos50=
=cos30+cos50-cos50=cos30=sqrt(3)/2