The number of solutions of the equation is, Trigonometric equation

Question

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 : [2024]

Smart Achievers · Accepted Answer

(1)

We have, $4 \sin^{2} x - 4 \cos^{3} x + 9 - 4 \cos x = 0$

$\Rightarrow 4 (1 - \cos^{2} x) - 4 \cos^{3} x + 9 - 4 \cos x = 0$

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

Ist clear that L.H.S. $\leq 12$ and never 13

$∴$ Solution does not exists.

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