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Question

If sin(y+z−x),sin(z+x−y),sin(x+y−z) are in A.P., then tanx,tany,tanz are in

A
A.P.
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B
G.P.
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C
H.P.
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D
none of these
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Solution

The correct option is D A.P.
As sin(y+zx),sin(x+zy),sin(y+xz)
sin(y+zx)+sin(y+xz)2=sin(x+zy)
2sinycos(zx)=2sin(x+zy)sinycos(zx)=sinycos(z+x)+sin(z+y)cosysiny(cos(zx)+cos(z+x))=sin(z+y)cosytanx+tanz=2tany

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