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 $195^{\circ }$
$=cos\left(270^{\circ }-15^{\circ }\right)+sin\left(180^{\circ }+15^{\circ }\right)$
$=-sin15^{\circ }-sin15^{\circ }$
$=-2sin15^{\circ }=-2\left(\frac{\sqrt{3}-1}{2\sqrt{2}}\right)=-\left(\frac{\sqrt{3}-1}{\sqrt{2}}\right)$