Setting functions equal to each other to cancel

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To solve the equation sin(3x) = 3sin(x), one approach is to express sin(3x) in terms of sin(x) using the identity sin(3x) = 3sin(x) - 4sin^3(x). This transforms the equation into 3sin(x) - 4sin^3(x) = 3sin(x), leading to the simplified form -4sin^3(x) = 0. Factoring gives sin^3(x) = 0, which implies that sin(x) = 0. The discussion emphasizes the importance of using trigonometric identities to rewrite and simplify the equation effectively.
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Homework Statement



sin(3x)=3sin(x)

Homework Equations





The Attempt at a Solution



How do you solve this for x?
 
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What identity can you replace sin(3x) with? (Hint: you want to write everything in terms of sinx)
 
Well I came up with;
(1+2cos(2x))sinx=3sinx

but that didn't work either
 
getty102 said:
Well I came up with;
(1+2cos(2x))sinx=3sinx

but that didn't work either


and you can replace cos(2x) by?
 

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