First slide

Compound angles

Question

If $2 \tan α + \cot β = \tan β$ , then the value of $\tan (β - α)$ is

Moderate

A

$\tan α$
B

$\cot α$
C

$\tan β$
D

$\cot β$

Solution

$\begin{array}{l} \tan (β - α) = \frac{\tan β - \tan α}{1 + \tan β \tan α} = \frac{\tan α + \cot β}{1 + \tan β \tan α} \\ = \frac{\tan α \tan β + 1}{\tan β (1 + \tan α \tan β)} \\ = \cot β \end{array}$

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