Question

Найдите значение выражения:
sin113cos323+cos247cos307

Answer 1

sin(113)*cos(323)=0.5*(sin(323+113))-sin(323-113))=0.5*(sin(76)-sin(210))

cos(247)*cos(307)=0.5*(cos(307-247)+cos(307+247))=0.5*(cos(60)+cos(194))

0.5*(sin(76)-sin(210)+cos(60)+cos(194))=

=0.5*(sin(76)+cos(194)-sin(210)+cos(60))=0.5*(cos(270+76)+cos(194)+sin(30)+cos(60))=

=0.5*(cos(346)+cos(194)+sin(30)+cos(60))=

=0.5*(cos(14)-cos(14)+cos(60)+cos(60))=0.5*(2*cos(60))=cos(60)=1/2