First slide

Multiple and sub- multiple Angles

Question

The value of cos 9°-sin 9°, is

Moderate

A

$\frac{5 + \sqrt{5}}{4}$
B

$\frac{\sqrt{5 - \sqrt{5}}}{2}$
C

$- \frac{\sqrt{5 - \sqrt{5}}}{2}$
D

none of these

Solution

We have,
$\begin{array}{l} \cos 9^{\circ} - \sin 9^{\circ} \\ = \sqrt{{(\cos 9^{\circ} - \sin 9^{\circ})}^{2}} \\ = \sqrt{1 - \sin 18^{\circ}} = \sqrt{1 - (\frac{\sqrt{5} - 1}{4})} = \sqrt{\frac{5 - \sqrt{5}}{2}} \end{array}$

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