First slide

Trigonometric equations

Question

The number of solutions of $12 \cos^{3} x - 7 \cos^{2} x + 4 \cos x = 9$ is

Moderate

A

0
B

2
C

infinite
D

none of these

Solution

The given equation is $(\cos x - 1) (12 \cos^{2} x + 5 \cos x + 9) = 0$
$\Rightarrow \cos x = 1$ only as the other factor gives imaginary roots
$\Rightarrow x = 2 nπ, n \in Z$
Hence, it has infinite solutions as $n \in Z$

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