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elvira1234123
@elvira1234123
July 2022
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sin1.5x+3sinx=3sin0.5x
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sharadi
Verified answer
Sin1.5x+3sinx=3sin0.5x
Sin1.5x+ (3sinx-3sin0.5x) = 0
Sin1,5x + 3(Sinx - Sin0,5x) = 0
Sin1,5x +3*2Sin0,25xCos0,75x = 0
2Sin0,75xCos0,75x + 6Sin0,25xCos0,75x = 0
Cos0,75x(Sin0,75x + 3Sin0,25x) = 0
Cos0,75x = 0 или Sin0,75x + 3Sin0,25x = 0
0,75x = π/2 + πk , k ∈Z 3Sin0,25x - 4Sin⁴0,25x + 3Sin0,25x =0
x = 2π/3 + 4πk/3, k∈Z
6Sin0,25x -4Sin⁴0,25x = 0
Sin0,25x(6 - 4Sin³0,25x) = 0
Sin0,25x = 0 или 6-4Sin³0,25x =0
0,25x = πn, n ∈Z или Sin³0,25x = 1,5
x = 4πn, n ∈Z
∅
1 votes
Thanks 2
elvira1234123
как получилась 4 строка?
sharadi
3 вынес за скобку, а в скобке разность синусов.
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Answers & Comments
Verified answer
Sin1.5x+3sinx=3sin0.5xSin1.5x+ (3sinx-3sin0.5x) = 0
Sin1,5x + 3(Sinx - Sin0,5x) = 0
Sin1,5x +3*2Sin0,25xCos0,75x = 0
2Sin0,75xCos0,75x + 6Sin0,25xCos0,75x = 0
Cos0,75x(Sin0,75x + 3Sin0,25x) = 0
Cos0,75x = 0 или Sin0,75x + 3Sin0,25x = 0
0,75x = π/2 + πk , k ∈Z 3Sin0,25x - 4Sin⁴0,25x + 3Sin0,25x =0
x = 2π/3 + 4πk/3, k∈Z 6Sin0,25x -4Sin⁴0,25x = 0
Sin0,25x(6 - 4Sin³0,25x) = 0
Sin0,25x = 0 или 6-4Sin³0,25x =0
0,25x = πn, n ∈Z или Sin³0,25x = 1,5
x = 4πn, n ∈Z ∅