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cherepov00
@cherepov00
June 2021
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Пожалуйста,помогите решить уравнение
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sedinalana
Sin5x-cos15x=0
sin5x+sin(π/2-15x)=0
2sin(10x-π/4)cos(-5x+π/4)=0
sin(10x-π/4)=0⇒10x-π/4=πk⇒10x=π/4+πk⇒x=π/40+πk/10,k∈z
cos(5x-π/4)=0⇒5x-π/4=π/2+πk⇒5x=3π/4+πk⇒x=3π/20+πk/5,k∈z
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Answers & Comments
sin5x+sin(π/2-15x)=0
2sin(10x-π/4)cos(-5x+π/4)=0
sin(10x-π/4)=0⇒10x-π/4=πk⇒10x=π/4+πk⇒x=π/40+πk/10,k∈z
cos(5x-π/4)=0⇒5x-π/4=π/2+πk⇒5x=3π/4+πk⇒x=3π/20+πk/5,k∈z