Question

10кл. решите a)cos66°cos 24° - sin24°sin66° б)sin24°sin54°+cos24°sin36°

Answer 1

1) по формуле суммы аргументов косинуса:
$cos66*cos24-sin24*sin66=cos(24+66)=cos90=0$

2) $sin24*sin54+cos24*sin36=sin24*sin(30+24)+cos24*sin(60-24)=sin24*(sin30*cos24+sin24*cos30)+cos24*(sin60*cos24-sin24*cos60)=sin24*(0.5*cos24+sin24* \frac{ \sqrt{3}}{2})+cos24*(\frac{ \sqrt{3}}{2})*cos24-sin24*0.5)=\frac{ \sqrt{3}}{2}*sin^{2}24+0.5*sin24*cos24+\frac{ \sqrt{3}}{2}*cos^{2}24-0.5*sin24*cos24=\frac{ \sqrt{3}}{2}*(sin^{2}24+cos^{2}24)=\frac{ \sqrt{3}}{2}$