Question

If sin (y+z-x),sin (z+x-y) and sin (x+y-z) are in A.P. then tan x,tan y and tan z are in​

Answer 1

a,b,c are in AP = = a-b=b-c. sin (-x+y+z) - sin (x-y+z) = sin (x-y+z) -sin (x+y-z) . 2sin (( -2x+2y)/2) cos ((2z)/2) =2sin ((-2y+2z)/2) cos ((2x)/2). sin (y-x) cos (z) =sin (z-y) cos (x). cosz(sinycosx -cosxsiny) (sinzcosy-cosysinz) cosx. 2coszsinycosx = sinzcosycosx + sinxcoszcosy. divide by cosxcosycosz: 2tany= t anz + tanx == tanx,tany, tanz are in AP.

Answer 2

Answer:

please refer the above pic

Hope you understand

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