sin x sin 2x sin 3x = 0.25 sin 4x...

Помеха7 @Помеха7

August 2022 1 9 Report

sin x sin 2x sin 3x = 0.25 sin 4x

Answers & Comments

o1l7eg17 $sin(x)sin(2x)sin(3x)=0.25*sin(4x)$
$sin(x)sin(2x)sin(3x)=\frac{1}{4}sin(4x)$
$sin(x)sin(2x)sin(3x)-\frac{1}{4}sin(4x)=0$
$\frac{1}{4}(4sin(x)sin(2x)sin(3x)-sin(4x))=0$
$4sin(x)sin(2x)sin(3x)-sin(4x)=0$
$-8cos(x)sin(\frac{\pi}{4}-2x)sin(x)sin(\frac{\pi}{4}+2x)=0$
$cos(x)sin(\frac{\pi}{4}-2x)sin(x)sin(\frac{\pi}{4}+2x)=0$
cos(x)=0 sin(π/4 -2x)=0 sin(x)=0 sin(π/4 +2x)=0
x=π/2 +πn;n∈Z π/4 -2x=πn;n∈Z x=πn;n∈Z π/4 +2x=πn;n∈Z
-2x=πn -π/4;n∈Z 2x=πn -π/4;n∈Z
x=π/8 -πn/2;n∈Z x=πn/2 -π/8;n∈Z

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