If x,y,z are in A.P. and {tan ^{ | vedclass

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

$2 y=x+z$         ....$(1)$

As $	an ^{-1} x, 	an ^{-1} y, 	an ^{-1} z$ in $A.P$

$\Rightarrow 2 	an ^{-1} y=	an ^{-

Vedclass · Accepted Answer

$x = y = z$

Vedclass · Answer

$2 y=x+z$         ....$(1)$

As $	an ^{-1} x, 	an ^{-1} y, 	an ^{-1} z$ in $A.P$

$\Rightarrow 2 	an ^{-1} y=	an ^{-1} \frac{x+z}{1-x z}$

$\frac{2 y}{1-y^{2}}=\frac{x+z}{1-x z}$

$\frac{x-z}{1-y^{2}}=\frac{x+z}{1-x z}$ by $( 1)$

$(x+z)\left\{\frac{1}{1-y^{2}}-\frac{1}{1-x z}ight\}=0$

$(x+z)=0$ or $1-x z=x-y^{2}$

$y^{2}=x z$

$\Rightarrow x, y, z$ in $GP.$

As $x, y, z$  $AP$  and  $ G P$

$\Rightarrow x=y=z$

If $x,y,z$ are in $A.P.$ and ${\tan ^{ - 1}}x,{\tan ^{ - 1}}y$ and ${\tan ^{ - 1}}z$ are also in other $A.P.$ then . . .

Similar Questions

Between $1$ and $31, m$ numbers have been inserted in such a way that the resulting sequence is an $A. P.$ and the ratio of $7^{\text {th }}$ and $(m-1)^{\text {th }}$ numbers is $5: 9 .$ Find the value of $m$

If $a_m$ denotes the mth term of an $A.P.$ then $a_m$ =

If ${a_1} = {a_2} = 2,\;{a_n} = {a_{n - 1}} - 1\;(n > 2)$, then ${a_5}$ is

The sequence $\frac{5}{{\sqrt 7 }}$, $\frac{6}{{\sqrt 7 }}$, $\sqrt 7 $, ....... is

Write the first five terms of the following sequence and obtain the corresponding series :

$a_{1}=-1, a_{n}=\frac{a_{n-1}}{n}, n\, \geq\, 2$