A) \[a,\ b,\ c\]are in A.P.
B) \[\cos A,\ \cos B,\ \cos C\]are in A.P.
C) \[\sin A,\ \sin B,\ \sin C\]are in A.P.
D) (a) and (c) both
Correct Answer: D
Solution :
Here \[\tan \frac{A}{2}\tan \frac{C}{2}=\frac{s-b}{s}\] \[\frac{5}{6}.\frac{2}{5}=\frac{s-b}{s}\Rightarrow 3s-3b=s\Rightarrow 2s=3b\] \[\Rightarrow \] \[a+b+c=3b\] or \[a+c=2b\]. \[\therefore \] a, b, c are in A.P., also sinA, sinB, sinC are in A.P.
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