A) \[\cos 7{}^\circ \]
B) \[\sin \,\,53{}^\circ \]
C) \[\cos \,\,53{}^\circ \]
D) \[\sin \,\,7{}^\circ \]
Correct Answer: C
Solution :
\[\frac{\sqrt{3}\cos 23{}^\circ -\sin 23{}^\circ }{2}=\frac{\sqrt{3}}{2}\cos 23{}^\circ -\frac{1}{2}\sin 23{}^\circ \] \[=\cos 30{}^\circ \cos 23{}^\circ -\sin 30{}^\circ \sin 23{}^\circ \] \[=\cos \,\,(30{}^\circ +23{}^\circ )=\cos 53{}^\circ \] \[[\because \cos \,\,(A+B)=\cos A\cos B-\sin A\sin B]\]
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