A) \[\frac{1}{2}\]
B) \[-1\]
C) \[1\]
D) \[0\]
Correct Answer: A
Solution :
| [a] We have, \[A=\sqrt{3}\] |
| \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\angle A=60{}^\circ \] \[[\tan 60{}^\circ =\sqrt{3}]\] |
| \[\Rightarrow \,\,\,\,\,\,\,\angle C=180{}^\circ -90{}^\circ -\angle A=90{}^\circ -60{}^\circ =30{}^\circ \] |
| \[\therefore \,\,\,\,\,\,\,\,\sin A\cdot \cos C-\cos A\cdot \sin C\] |
| \[=\sin 60{}^\circ \cdot \cos 30{}^\circ -\cos 60{}^\circ \cdot \sin 30{}^\circ \] |
| \[=\frac{\sqrt{3}}{2}\times \frac{\sqrt{3}}{2}-\frac{1}{2}\times \frac{1}{2}=\frac{3}{4}-\frac{1}{4}=\frac{2}{4}=\frac{1}{2}\] |
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