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Q.
The number of solutions to the equation $12 \cos ^{3} x-7 \cos ^{2} x+4 \cos x=9$ is
Trigonometric Functions
Solution:
The given equation is $(\cos x-1)\left(12 \cos ^{2} x+5 \cos x+9\right)=0$
$\Rightarrow \cos x=1$ only as the other factor gives imaginary roots
$\Rightarrow \cos x=1 \Rightarrow x=2 n \pi$
Hence, it has infinite solutions as $n \in Z$.