Question

Помогите, прошу!
Вычислите:
1)Sin23*sin53+sin67*sin37
2(sin75*cos35+cos125*cos75)/sin40

Answer 1

$1); ; sin23cdot sin53+sin67cdot sin37=\\=sin(90-67)cdot sin53+sin67cdot sin(90-53)=\\=cos67cdot sin53+sin67cdot cos53=sin(67+53)=\\=sin120=sin(180-60)=sin60=frac{sqrt3}{2}$

$2); ; frac{sin75cdot cos35+cos125cdot cos75}{cos40} =[; cos125=cos(90+35)=-sin35; ]=\\= frac{sin75cdot cos35-sin35cdot cos75}{cos40} = frac{sin(75-35)}{cos40}=frac{sin40}{cos40}=tg40$