Предмет: Алгебра, автор: gnoevskayakris

cos6x+sin6x корень из 2 cos(3пи-3х)=1

Ответы

Автор ответа: safin1ilya

Cos6x+√2cos(3п/2-3х)=1
Cos6x-√2sin3x=1
1-2sin^2(3x)-√2sin3x=1
-2sin^2(3x)-√2sin3x=0
sin3x(-2sin3x-√2)=0
sin3x=0
3x=пn,n€z
x=пn/3,n€z
-2sin3x-√2=0
sin3x=-√2/2
3x=(-1)^n+1 п/4+пn,n€z
x=1/3*(-1)^n+1 п/4+пn/3,n€z

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