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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