A) A.P.
B) G.P.
C) H.P.
D) None of these
Correct Answer: A
Solution :
\[\frac{\sin A-\sin C}{\cos C-\cos A}=\cot B\]Þ\[\frac{2\cos \frac{A+C}{2}\sin \frac{A-C}{2}}{2\sin \frac{A+C}{2}\sin \frac{A-C}{2}}=\cot B\] \[\Rightarrow \cot \frac{(A+C)}{2}=\cot B\] Þ \[B=\frac{A+C}{2}\] Thus A, B, C will be in A.P.
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