First slide

Trigonometric equations

Question

The general solution of $\cos x \cos 6 x + 1 = 0$ is

Easy

A

$x = (2 n + 1) π, n \in z$
B

$x = 2 n π, n \in z$
C

$x = n π, n \in z$
D

none of these

Solution

We have $2 \cos x \cos 6 x = - 2$
$\Rightarrow \cos 7 x + \cos 5 x = - 2$
$\Rightarrow \cos 7 x = - 1 a n d \cos 5 x = - 1$
$\Rightarrow x = 2 n π + π, n \in Z$

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