If `sin(y+z-x),sin(z+x-y),"sin"(x+y-z)` are in A.P., then `t a n x ,tany ,tanz` are in (a)A.P. (b) G.P. (c) H.P. (d) none of these

Explanation

As `sin(y+z-x),sin(z+x-y) and sin(x+y-z)` are in A.P.

`:. sin(z+x-y)-sin(y+z-x) = sin(x+y-z)-sin(z+x-y)`

`=>2coszsin(x-y) = 2cosxsin(y-z)`

`=>coszsin(x-y) = cosxsin(y-z)`

`=>(coszsin(x-y))/(cosxcosycosz) = (cosxsin(y-z))/(cosxcosycosz)`

`=>(sin(x-y))/(cosxcosy) = (sin(y-z))/(cosycosz)`

Using `(sin(A-B))/(cosAcosB) = tanA-tanB`

`=>tanx-tany = tany - taz`

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