tan-1x,tan-1y,tan-1z..are in A.P and x,y,z are also in A.P ( y being not equal to 0,1 or -1)then ...... a)x,y,z are in G.P b)x=2y=z c)N.O.T
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3 Answers
1357x=y=z
so x,y,z are in GP too
Dwijaraj Paul Chowdhury This is a question from this year's JEE MAINSUpvote·0· Reply ·2013-06-08 01:43:27
Shalin Saurav may be but it is a question from arihant objective...- Shalin Saurav sir can u explain a bit more plz
2292y=x+z
2tan-1y=tan-1x+tan-1z
=> tan-1(2y1-y2)=tan-1 (x+z1-xz)
=>(2y1-y2)= (x+z1-xz)
Since 2y=x+z
11-y2=11-xz
=> y2=xz
Replacing y with x+z2
(x+z)2=4xz
:. (x-z)2=0
:.x=z
2y=x+z
:. y=x=z
:. They are in GP
2292y=x+z
2tan-1y=tan-1x+tan-1z
=> tan-1(2y1-y2)=tan-1 (x+z1-xz)
=>(2y1-y2)= (x+z1-xz)
Since 2y=x+z
11-y2=11-xz
=> y2=xz
Replacing y with x+z2
(x+z)2=4xz
:. (x-z)2=0
:.x=z
2y=x+z
:. y=x=z
:. They are in GP
- Dwijaraj Paul Chowdhury Sorry :/