Number of solutions of equation 4 sin ^2 x-4 cos ^3 mathrm{x}+9-4 cos mathrm{x}=0 ; mathrm{x} ∈[-2

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Trigonometrical Equations

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The number of solutions of the equation $4 \sin ^2 x-4$ $\cos ^3 \mathrm{x}+9-4 \cos \mathrm{x}=0 ; \mathrm{x} \in[-2 \pi, 2 \pi]$ is :

A

$1$

B

$3$

C

$2$

D

$0$

(JEE MAIN-2024)

Solution

$ 4 \sin ^2 x-4 \cos ^3 x+9-4 \cos x=0 ; x \in[-2 \pi, 2 \pi] $

$ 4-4 \cos ^2 x-4 \cos ^3 x+9-4 \cos x=0 $

$ 4 \cos ^3 x+4 \cos ^2 x+4 \cos x-13=0 $

$ 4 \cos ^3 x+4 \cos ^2 x+4 \cos x=13 $

$ \text { L.H.S. } \leq 12 \text { can't be equal to } 13 .$

Standard 11

Mathematics

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