Вычислите[latex]cos \frac{11 \pi }{56} cos \frac{3 \pi }{56} -sin \frac{11 \pi }{42}sin \frac{17 \pi }{42} [/latex]
Вычислите
[latex]cos \frac{11 \pi }{56} cos \frac{3 \pi }{56} -sin \frac{11 \pi }{42}sin \frac{17 \pi }{42} [/latex]
Гость
Ответ(ы) на вопрос:
Гостьcos11π/56cos3π/56=1/2[cos(11π/56-3π/56)+cos(11π/56+3π/56)]=
=1/2(cosπ/7+cosπ/4)
sin11π/42sin17π/42=1/2[cos(11π/42-17π/42)-cos(11π/42+17π/42)]=
=1/2(cos(-π/7)-cos2π/3)=1/2(cosπ/7+cosπ/3)
cos11π/56cos3π/56-sin11π/42sin17π/42=1/2cosπ/7+1/2cosπ/4-1/2cosπ/7-
-1/2cosπ/3=1/2cosπ/4-1/2cosπ/3=1/2(√2/2-1/2)=(√2-1)/4
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