If p,q,r are in G.P and {tan ^{ - 1}}p, {tan | vedclass

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Question

(a) $p,q,r \in {m{G}}{m{.}}\,{m{P}}{m{.}}$, $	herefore {q^2} = pr$

Also ${	an ^{ - 1}}p,{	an ^{ - 1}}q,$ ${	an ^{ - 1}}r \in $ $A.P.$

Vedclass · Accepted Answer

$p = q = r$

Vedclass · Answer

(a) $p,q,r \in {m{G}}{m{.}}\,{m{P}}{m{.}}$, $	herefore {q^2} = pr$

Also ${	an ^{ - 1}}p,{	an ^{ - 1}}q,$ ${	an ^{ - 1}}r \in $ $A.P.$

==> ${	an ^{ - 1}}p + {	an ^{ - 1}}r = 2{	an ^{ - 1}}q$

==> $p + r = 2q \Rightarrow p,q,r$ are in $A.P.$

Now $p, q, r$ are both in $A.P$ and $G.P.,$

which is possible only, if $p = q = r$.

If $p,q,r$ are in $G.P$ and ${\tan ^{ - 1}}p$, ${\tan ^{ - 1}}q,{\tan ^{ - 1}}r$ are in $A.P.$ then $p, q, r$ are satisfies the relation

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