In the `!ABC` , the altitudes are in H.P., then

Options

A. angles A,B,C are in A.P.
B. sides a,b,c are in A.P.
C. sinA,sinB,sinC are in A.P
D. none of these

Explanation

Let `p_(1), p_(2), p_(3)` be the altitudes on sides BC, CA and AB respectively. Then,
`Delta=1/2ap_(1),Delta=1/2bp_(2)` and `Delta=1/2cp_(3)`
`thereforep_(1)=(2Delta)/a=(2Delta)/(2RsinA)=(Delta)/(RsinA)`
Similarly, we have
`p_(2)=(Delta)/(RsinB)` and `p_(3)=(Delta)/(RsinC)`
Now,
`p_(1),p_(2),p_(3)` are in H.P.

`rArr1/(p_(1)),1/(p_(2)),1/(p_(3))` are in A.P.
`rArr(RsinA)/(Delta),(RsinB)/(Delta),(RsinC)/(Delta)` are in A.P.
`rArr` sin A, sin B, sin C are in A.P.