inverse trigo.

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

3 Answers

1357
Manish Shankar ·

x=y=z
so x,y,z are in GP too

229
Dwijaraj Paul Chowdhury ·

2y=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

229
Dwijaraj Paul Chowdhury ·

2y=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

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