Question

The value of cos $255^{\circ}$ + sin $195^{\circ}$ is

• A. $\frac{\sqrt{3}-1}{2\sqrt{2}}$
• B. $\frac{\sqrt{3}+1}{\sqrt{2}}$
• C. $\frac{\sqrt{3}-1}{\sqrt{2}}$
• D. $\frac{\sqrt{3}}{\sqrt{2}}$

Answer 1

Answer: (C)

Consider cos $255^{\circ}$ + sin $195^{\circ}$
$= cos \left(270^{\circ} -15^{\circ}\right) + sin \left(180^{\circ} +15^{\circ}\right)$
$= -sin 15^{\circ}-sin 15^{\circ}$
$= -2 sin 15^{\circ} = -2 \left(\frac{\sqrt{3}-1}{2\sqrt{2}}\right) = -\left(\frac{\sqrt{3}-1}{\sqrt{2}}\right)$