A) 0
B) \[\sqrt{(3/2)}\]
C) \[\frac{1}{\sqrt{2}}\]
D) \[\left( \sqrt{3+\frac{1}{2}} \right)\]
Correct Answer: C
Solution :
\[\cos 105{}^\circ +\sin 105{}^\circ \] \[=\]\[\cos (60{}^\circ +45{}^\circ )+\sin (60{}^\circ +45{}^\circ )\] \[+(\sin 60{}^\circ \cos 45{}^\circ +\cos 60{}^\circ \sin 45{}^\circ )\] \[=\]\[\left( \frac{1}{2}\cdot \frac{1}{\sqrt{2}}-\frac{\sqrt{3}}{2}\cdot \frac{1}{\sqrt{2}} \right)+\frac{\sqrt{3}}{2}\cdot \frac{1}{\sqrt{2}}+\frac{1}{2}\cdot \frac{1}{\sqrt{2}}\] \[=\]\[\frac{2}{2\sqrt{2}}=\frac{1}{\sqrt{2}}\]
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