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Question

Let α,β,γ be in AP and x,y,z be in GP. If tanα=x,tanβ=y and tanγ=z, then

A
x=y=z
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B
xz=1
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C
x=y=z1
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D
x,y,z are in AP
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Solution

The correct option is D x,y,z are in AP
x,y,z are in GP.
y2=xz

α,β,γ are in AP.
2β=α+γ
tan(2β)=tan(α+γ)
2tanβ1tan2β=tanα+tanγ1tanαtanγ
2y1y2=x+z1xz
2y=x+z and y1
x,y,z are in AP.
Since, x,y,z are in AP and GP,
x,y,z is a constant sequence.



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