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  4. (3 cos θ+ cos 3 θ/3 sin θ- sin 3 θ) is equal to

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Q. $\frac{3 \cos \theta+\cos 3 \theta}{3 \sin \theta-\sin 3 \theta}$ is equal to

Trigonometric Functions

Solution:

$\frac{3 \cos \theta+4 \cos ^3 \theta-3 \cos \theta}{3 \sin \theta-\left(3 \sin \theta-4 \sin ^3 \theta\right)}=\frac{4 \cos ^3 \theta}{4 \sin ^3 \theta}=\cot ^3 \theta$