sin9x+sin5x =5cos2x решать ур- ие. Created by seva162. matematika-ru

sin9x+sin5x =5cos2x решать ур- ие...

July 2022 1 10 Report

sin9x+sin5x =5cos2x решать ур- ие

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atursynkazina2003 Sinx + sin5x = sqrt(5) * cos2x
-------------------------------------
Sinx + sin5x = 2 * sin ((x+5x)/2) * сos ((5x-x)/2) = 2 * sin3x * cos 2x
-------------------------------------
2 * sin3x * cos 2x - sqrt(5) * cos2x = 0
cos2x * (2 * sin3x - sqrt(5)) = 0
1) cos2x = 0
2x = pi/2 + pi*n (n ∈ z)
x = pi/4 + (pi*n)/2 (n ∈ z)
2)2 * sin3x - sqrt(5) = 0
sin3x = sqrt(5)/2
3x = (-1)^n * arcsin sqrt(5)/2 + pi*n (n ∈ z)
x = (-1)^n * (arcsin sqrt(5)/2)/3 + (pi*n)/3 (n ∈ z)

P.s. Точно в условии корень из 5 стоит?

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seva162 Нет Без Корня

seva162 Ответ не то

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