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I've got this far but don't understand where the $2$ on the numerator comes from: $$\dfrac{\sin a \cos b + \cos a \sin b}{\sin b \cos b}\overset{?}{=}\dfrac{\sin(a+b)}{\sin 2b}$$

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    The double-angle identity is $\sin 2b = 2\sin b \cos b$ (not $\sin b \cos b$). So once you get $\frac{\sin a \cos b + \cos a \sin b}{\sin b \cos b} = \frac{\sin (a+b)}{\sin b \cos b}$, multiply the numerator and denominator by $2$ and use the double-angle identity I just mentioned.2012-01-15
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    so do you times everything by 2? I don't really get it2012-01-15

2 Answers 2