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  4. The value(s) of θ, which satisfy the equation: 2 cos 3 3 θ+3 cos 3 θ+4=3 sin 2 3 θ is/are -

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Q. The value(s) of $\theta$, which satisfy the equation : $2 \cos ^3 3 \theta+3 \cos 3 \theta+4=3 \sin ^2 3 \theta$ is/are -

Trigonometric Functions

Solution:

$2 \cos ^3 3 \theta+3 \cos 3 \theta+4-3 \sin ^2 3 \theta$
$\Rightarrow \left(\cos 3 \theta+\frac{1}{2}\right)\left(2 \cos ^2 3 \theta+2 \cos 3 \theta+2\right)=0$
$\Rightarrow \cos 3 \theta=-\frac{1}{2} \Rightarrow 3 \theta=2 n \pi \pm \frac{2 \pi}{3}$
$\Rightarrow \theta=\frac{2 n \pi}{3} \pm \frac{2 \pi}{9}$