Question

hey frnds plz answer this question......

I have exam tomorrow....

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−cosysinx) = (sinzcosy−coszsiny)cosx
2coszsinycosx = sinzcosycosx + sinxcoszcosy
Divide by cosxcosycosz : 2tany = tanz+tanx <==> tanx, tany, tanz are in AP