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1 \(\cos \left ( A+B\right ) \) and \(\sin \left ( A+B\right ) \)
2 \(\cos \left ( A-B\right ) \) and \(\sin \left ( A-B\right ) \)
3 \(\cos \left ( 2A\right ) \) and \(\sin \left ( 2A\right ) \)
4 \(\cos \left ( \frac {x}{2}\right ) \)
5 \(\sin \left ( \frac {x}{2}\right ) \)
6 \(\sin \left ( \alpha \right ) +\sin \left ( \beta \right ) \)
7 \(\cos \left ( \alpha \right ) +\cos \left ( \beta \right ) \)
8 \(\sin \left ( \alpha \right ) -\sin \left ( \beta \right ) \)
9 \(\cos \left ( \alpha \right ) -\cos \left ( \beta \right ) \)
10 \(\cos \left ( A\right ) \cos \left ( B\right ) \)
11 \(\sin \left ( A\right ) \cos \left ( B\right ) \)
12 \(\sin \left ( A\right ) \sin \left ( B\right ) \)

To derive trig identities (something useful in the exam), we will use Euler relation as starting point, which is \(e^{ix}=\cos x+i\sin x\).

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