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Question

If tan1x,tan1y,tan1z are in A.P. , then 2y1y2=

A
xz1+xz
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B
x+z1xz
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C
x+z
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D
xy
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Solution

The correct option is B x+z1xz
If tan1x,tan1y,tan1z are inA.P

2tan1y=tan1x+tan1z

take \tan on both sides,

tan(2tan1y)=tan(tan1x+tan1z)

2tantan1y1(tantan1y)=(tantan1x+tantan1z1tantan1xtantan1z)

2y1y2=x+z1xy[tan(A+B)=tanA+tanB1tanAtanB,tantan1x=x]

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