MCQ
If $\frac{{\sin A - \sin C}}{{\cos C - \cos A}} = \cot B,$ then $A,B,C$ are in
- ✓$A.P.$
- B$G.P.$
- C$H.P.$
- DNone of these
✓
Answer
Correct option: A.
$A.P.$
a
(a) $\frac{{\sin A - \sin C}}{{\cos C - \cos A}} = \cot B$
(a) $\frac{{\sin A - \sin C}}{{\cos C - \cos A}} = \cot B$
==>$\frac{{2\cos \frac{{A + C}}{2}\sin \frac{{A - C}}{2}}}{{2\sin \frac{{A + C}}{2}\sin \frac{{A - C}}{2}}} = \cot B$
$ \Rightarrow \cot \frac{{(A + C)}}{2} = \cot B$
==> $B = \frac{{A + C}}{2}$
Thus $A, B, C$ will be in $A.P.$
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