First slide

Trigonometric transformations

Question

Let $f (n) = 2 \cos n x, \forall n \in N,$ then $f (1) f (n + 1) - f (n)$ is equal to

Moderate

A

$f (n + 3)$
B

$f (n + 2)$
C

$f (n + 1) f (2)$
D

$f (n + 2) f (2)$

Solution

$f (n) = 2 \cos n x \Rightarrow f (1) f (n + 1) - f (n)$
$= 4 \cos x \cos (n + 1) x - 2 \cos n x$
$= 2 \cos (n + 2) x = f (n + 2)$

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