A) \[\frac{1}{\sqrt{2}}\]
B) \[1\]
C) \[0\]
D) \[\sqrt{2}\]
Correct Answer: C
Solution :
\[\sin \,(45{}^\circ +A)-\cos \,\,(45{}^\circ -A)\] \[=(\sin 45{}^\circ \cos A+\cos 45{}^\circ \sin A)\] \[-\,\,[\cos 45{}^\circ \cos A+\sin A\sin 45{}^\circ ]\] \[=\frac{\cos A}{\sqrt{2}}+\frac{\sin A}{\sqrt{2}}-\frac{\cos A}{\sqrt{2}}-\frac{\sin A}{\sqrt{2}}=0\]
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