Question

Пожалуйста помогите
0,5sin40-cos30+cos20cos10

Answer 1

cos20°cos10°=(1/2)( cos(20°+10°)·cos(20°-10°))= (1/2)cos30°+(1/2)cos10°

Тогда
0,5·sin40°-cos30°+ cos20°·cos10°=

=0,5·sin40°-cos30° +(1/2)cos30°+(1/2)cos10°

=0,5·sin40°+0,5сos10°-0,5cos30°=

=0,5sin40°+0,5·(cos10°-cos30°)=

=0,5sin40°+0,5·2sin((10°+30°)/2)sin((30°-10°)/2)

=0,5·2sin20°cos20°+sin20°·sin10°=

=sin20°·(cos20°+sin10°)