Question

Помогите решить примеры:

) sin 107°×sin167°+sin 197°×sin 257°
2)4sin10°×sin30°×sin50°×sin70°
3)7/√3×sin18°×sin54°×sin60°

Answer 1

1
sin107*sin167+sin197*sin257=sin(90+17)*sin(180-13)+sin(180+17)*sin(270-13)=cos17*sin13-sin17*(-cos13)=sin13*cos17+sin17cos13=sin(13+17)=sin30=1/2
2
4sin10*sin30*sin50*sin70=4sin10*1/2*sin50*sin70=2sin10*sin50*sin70=
=2*sin10*1/2*(cos(70-50)-cos(70+50))=sin10*(cos20-cos120)=
=sin10(cos20+1/2)
3
7/√3*√3/2*sin18*sin54=3,5*sin18*sin54=3,5sin18cos36