Question

Упростите cos(60+b)*cos(60-b)-sin(60-b)*sin(60+b)

Answer 1

$cos(60+b)*cos(60-b)-sin(60-b)*sin(60+b)=$$\frac{cos(60+b+60-b)+cos(60+b-60+b)}{2} - \frac{cos(60+b-60+b)-cos(60+b+60-b)}{2} =$$\frac{cos120+cos2b}{2} - \frac{cos2b-cos120}{2} =\frac{cos120+cos2b-cos2b+cos120}{2}=cos120=- \frac{1}{2}$