Задача 61628 sinxsin3x+sin4xsin8x=0...

6196369b45bee26935299707

18.11.2021 14:19:41

sinxsin3x+sin4xsin8x=0

6196984b61acd962013bfacf

18.11.2021 21:23:09

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1/2*(cos(x-3x)-cos(x+3x)+cos(4x-8x)-cos(4x+8x))=
=1/2(cos2x-cos4x+cos4x-cos12x)=1/2(cos2x-cos12x)=1/2*(-2)sin7xsin5x=0
sin7x=0⇒7x=πn⇒x=πn/7
sin5x=0⇒5x=πn⇒x=πn/5