Question

Complete the identity
sin(a-b)/cos a cos b=?

Answer 1

Answer on Question #81508 – Math – Trigonometry

Question

Complete the identity?

$\sin(a-b)/\cosacosb =$

$$\frac{\sin(a - b)}{\cos a \cos b} =$$

Solution

$$\frac{\sin(a - b)}{\cos a \cos b} = \frac{\sin a \cdot \cos b - \cos a \cdot \sin b}{\cos a \cdot \cos b} = \frac{\sin a \cdot \cos b}{\cos a \cdot \cos b} - \frac{\cos a \cdot \sin b}{\cos a \cdot \cos b} = \frac{\sin a}{\cos a} - \frac{\sin b}{\cos b} = \tan a - \tan b$$

**Answer:** $\frac{\sin(a - b)}{\cos a \cos b} = \tan a - \tan b.$

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