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lim(xto0) (sin(alpha+beta)x+sin(alpha-be...

`lim_(xto0) (sin(alpha+beta)x+sin(alpha-beta)x+sin2alphax)/(cos2betax-cos2alphax).x`

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To solve the limit \[ \lim_{x \to 0} \frac{\sin((\alpha + \beta)x) + \sin((\alpha - \beta)x) + \sin(2\alpha x)}{\cos(2\beta x) - \cos(2\alpha x)} \cdot x, \] we can start by analyzing the numerator and the denominator separately as \(x\) approaches 0. ...
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