The number of solutions of the equation 4 sin 2 x-4 cos 3 x +9-4 cos x =0 ; x in[-2 π, 2 π] is :

Mathematics · Trigonometry Ratios and Identities

JEE Main 2024 — 1 February, Shift 2 — Question 3

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 :

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

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

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

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

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

Answer key and solution verified before publishing.

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