First slide

Trigonometric Identities

Question

The value of $\sin 255^{0} + \cos 165^{0}$ is

Moderate

A

0
B

$\frac{\sqrt{3} - 1}{\sqrt{3}}$
C

$\frac{- (\sqrt{3} + 1)}{\sqrt{2}}$
D

$\frac{\sqrt{2} + 1}{\sqrt{2}}$

Solution

$\sin (270^{0} - 15^{0}) + \cos (180^{0} - 15^{0})$
$= - \cos 15^{0} - \cos 15^{0} = - 2 \cos 15^{0}$

$= - 2 \frac{(\sqrt{3} + 1)}{2 \sqrt{2}}$ $= - \frac{(\sqrt{3} + 1)}{\sqrt{2}}$

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