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Find all the number 'a' for which any ro...

Find all the number 'a' for which any root of the equation ` sin 3x =a sin x +(4-2|a|)sin^(2) x ` is a root of the equation ` sin 3x + cos 2 x =1+2 sinx cos 2x ` and any root of the latter equation is a root of the former .

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The correct Answer is:
`a in [1,5]`
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