If in a triangle ABC, `(sinA)/(sinC) = (sin(A-B))/(sin(B-C))`, then

Options

A. A.P
B. G.P.
C. H.P.
D. none of these

Explanation

We have,
sin A: sin C = sin (A -B): sin (B-C)
`rArrsin (B +C): sin (A+ B) =sin (A-B): sin (B-C)`
`rArrsin (B +C) sin (B-C) = sin (A+ B) sin (A -B)`
`rArrsin^(2)B-sin^(2)C=sin^(2)A-sin^(2)B`
`rArr2sin^(2)B=sin^(2)A+sin^(2)C`
`rArr2b^(2)=a^(2)+c^(2)` [Using Sine rule]
`rArra^(2),b^(2),c^(2)` are in A.P.