analearLurk analearLurk

24-11-2016
Mathematics

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Solve sin2x + 4sin x + 3 = 0

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HomertheGenius HomertheGenius

25-11-2016

sin² x + 4 sin x + 3 = 0
Substitution: u = sin x
u² + 4 u + 3 = 0
u² + 3 u + u + 3 = 0
u ( u + 3 ) + ( u + 3 ) = 0
( u + 3 ) ( u + 1 ) = 0
u = - 3, u = - 1;
sin x = - 3 ( false )
sin x = - 1
Answer:
x = 3 π / 2 + 2 k π , k ∈ Z

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