First slide

Compound angles

Question

$\cot θ - \cot 3 θ$ is equal to

Moderate

A

$2 \sin θ \sin 3 θ$
B

$2 \cos θ \cos 3 θ$
C

$2 \cos θ cosec 3 θ$
D

$2 \sin θ cosec 3 θ$

Solution

$\begin{array}{l} \cot θ - \cot 3 θ = \frac{\cos θ \sin 3 θ - \sin θ \cos 3 θ}{\sin θ \sin 3 θ} \\ = \frac{\sin 2 θ}{\sin θ \sin 3 θ} \\ = 2 \cos θ cosec 3 θ . \end{array}$

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