Question

5 sin 3x - 9 sin x = 0

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Answer 1

5sin3x - 9sin x = 0

5(3sinx  - 4sin^3 x) - 9sinx = 0

15sinx - 20sin^3 x - 9 sinx = 0

6sinx - 20sin^3 x = 0
2sinx (3 -10sin^2 x) = 0
a) 2sinx = 0

sinx = 0 
x1= πn
б) 3 - 10sin^2 x = 0

10sin^2x = 3
sin^2x = 3/10
sinx = +-√(3/10)

sinx = √(3/10)
x2 = (-1)^n * arcsin(3/10)+πn

sinx = -√(3/10)
x3 = (-1)^(n+1) * arcsin(3/10)+πn