Решить уравнение sin(2x-7pi/2)+sin(3pi/2-8x)+cos(6x)=1. Created by Alexandra47. algebra-ru

2-8x)+cos(6x)=1...

Alexandra47 @Alexandra47

August 2022 1 15 Report

Решить уравнение sin(2x-7pi/2)+sin(3pi/2-8x)+cos(6x)=1

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oganesbagoyan

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Sin(2x -7π/2) +sin(3π/2 -8x) +cos6x =1;
sin(-(7π/2 -2x)) -cos8x+cos6x =1 ;
-sin(7π/2 -2x) -cos8x+cos6x =1 ;
* * *sin(7π/2 -2x) =  sin(4π-(π/2 +2x)) = -sin(π/2 +2x) = -cos2x * * *
cos2x -cos8x +cos6x -1 =0 ;
cos6x +cos2x -(1+cos8x) =0 ;  * * *или cos2x -cos8x -(1-cos6x) =0 * * *
2cos4xcos2x -2cos²4x =0 ;
2cos4x(cos2x -cos4x) =0 ;
2cos4x*2sinx*sin3x =0 ;
4sinx*sin3x*cos4x=0 ;
[sinx =0 ; sin3x =0 ; cos3x =0 .
[ x=πk ; x=πk/3 ; 3x =π/2 +πk , k∈Z.
объединяя решении :
[x = πk/3 ; x =π/6 + (π/3)* k   , k∈Z.

ответ : πk/3 ; x =π/6 +(π/3)* k , k∈Z.

8 votes Thanks 5

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Alexandra47 July 2022 | 0 Ответы

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Alexandra47 July 2022 | 0 Ответы

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Answers & Comments

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