First slide

Compound angles

Question

$\frac{\cos 11^{\circ} - \sin 11^{\circ}}{\cos 11^{\circ} + \sin 11^{\circ}}$ is equal to

Moderate

A

$\cot 56^{\circ}$
B

$t an 11^{\circ}$
C

$\tan 56^{\circ}$
D

$\cot 11^{\circ}$

Solution

$\begin{array}{l} \frac{\cos 11^{\circ} - \sin 11^{\circ}}{\cos 11^{\circ} + \sin 11^{\circ}} = \frac{\cos 11^{\circ} + \cos (90^{\circ} + 11^{\circ})}{\cos 11^{\circ} - \cos (90^{\circ} + 11^{\circ})} \\ = \frac{2 \cos 56^{\circ} \cos 45^{\circ}}{2 \sin 56^{\circ} \sin 45^{\circ}} = \cot 56^{\circ} \end{array}$

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