A) \[\frac{1}{2}\]
B) 1
C) \[\sqrt{2}\]
D) \[\frac{1}{\sqrt{2}}\]
Correct Answer: D
Solution :
\[\cos 105{}^\circ +\sin 105{}^\circ =\cos (90{}^\circ +15{}^\circ )+\sin (90{}^\circ +15{}^\circ )\] =\[\cos 15{}^\circ -\sin 15{}^\circ =\frac{\sqrt{3}+1}{2\sqrt{2}}-\frac{\sqrt{3}-1}{2\sqrt{2}}=\frac{2}{2\sqrt{2}}=\frac{1}{\sqrt{2}}\].
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