First slide

Compound angles

Question

$\cos ((n + 1) α) \cos ((n - 1) α) + \sin ((n + 1) α) \sin ((n - 1) α) =$

Moderate

A

$\cos 2 n α$
B

$\sin 2 n α$
C

$\cos 2 α$
D

$\sin 2 α$

Solution

cos(A-B)=cosAcosB+sinAsinB
$\cos (n α + α - n α + α) = \cos 2 α$

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