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I am to simplify this expression:

$$\sin{1}\cos{2}+\cos{1}\sin{2}$$

This is a notes problem which wants to work with the formulas for $\cos{(\alpha+\beta)}$ or $\sin{(\alpha+\beta)}$ but being that I missed the day, I'm solidly confused. Hints and explanations would be much appreciated.

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  • $\begingroup$ You can use $\sin(x+y)=\sin x\cos y+\cos x \sin y$. $\endgroup$ – user84413 Apr 28 '15 at 23:53
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$Sin(x+y)=Sin\ (x) \ Cos(y)+\ Sin (y)\ Cos (x) $

which is the same as $Sin(\alpha+\beta)=sin(\alpha)cos(\beta)+sin(\beta)cos(\alpha)$

This is the addition formula for sine.

so it is just a simple application. it is of the form Sin(1+2)=Sin(3)

because you have $sin(\alpha+\beta)=sin(1)cos(2)+cos(1)sin(2)$

comparing to the formula, you see that in your case $\alpha=1$ and $\beta=2$ , but the order does not matter.

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