If in `Delta ABC,` the altitudes from the vertices A, B and C on opposite sides are in HP, then sin A sin B and sin C are in

Options

A. H.P.
B. AGP
C. A.P.
D. G.P.

Explanation

We have,
`Delta=1/2ap_(1)=1/2bp_(2)=1/2cp_(3)`
`rArra=(2Delta)/(p_(1)).b=(2Delta)/(p_(2))` and `c=(2Delta)/(p_(3))`
It JS given that
`p_(1),p_(2),p_(3)` are in H.P.
`rArr1/(p_(1)),1/(p_(2)),1/(p_(3))` are in A.P.
`rArr(2Delta)/(p_(1)),(2Delta)/(p_(2)),(2Delta)/(p_(3))` are in A.P.
`rArr`a, b, c are in A.P.
`rArr` sin A, sin B, sin C are iin A.P.