корень из cos2x -cosx=0. Created by vikamolchanova1. algebra-ru

корень из cos2x -cosx=0...

August 2022 1 10 Report

корень из cos2x -cosx=0

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sedinalana √cos2x-cosx=0
√cos2x=cosx
cosx≥0⇒x∈([-π/2+2πk;π/2+2πk,k∈z
возведем в квадрат
cos2x=cos²x
2cos²x-1-cos²x=0
cos²x-1=0
cos²x=1
cosx=-1⇒x=π+2πk,k∈z не удов усл
cosx=1⇒x=2πk,k∈z

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