ПОМОГИТЕ решить уравнение sinx+cosx=[tex] \frac{1}{5} [/tex]. Created by Masha04120. algebra-ru

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Masha04120 @Masha04120

July 2022 1 12 Report

ПОМОГИТЕ решить уравнение
sinx+cosx=[tex] \frac{1}{5} [/tex]

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oganesbagoyan

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Решить уравнение sinx+cosx= 1/5
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cosx +sinx = 1/5 ; * * * sinπ/4 =cosπ/4 =1/√2 * * *
(1/√2)*cosx+1/√2) *sinx = 1/5√2 ;
cosx*cos(π/4)+ sinx*sin(π/4) = √2/10 ;
* * * cos(α -β) =cosα*cosβ - sinα*sinβ * * *
cos(x -π/4) = √2/10 ;
x -π/4 = ±arccos(√2/10) +2πn , n∈Z ;
x =π/4 ±arccos(√2/10) +2πn , n∈Z ;

ответ : π/4 ±arccos(√2/10) +2πn , n∈Z ;
.

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