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If p,q,r are in G.P and tan^(-1)p,tan^(-...

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` satisfies the relation

A

`p=q=r`

B

`p!= q!=r`

C

`p+q=r`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
a
Since , ` 2 tan ^(-1) q = tan^(-1)p+tan^(-1) r`
` rArr tan^(-1). (2q)/(1-q^(2)) = tan^(-1) (p+r)/(1-p" "r)`
` rArr 2q = p+r" " [ :' q^(2)=pr]` ,brgt ` rArr` p,q,r are in Ap.
But p,q,r are in GP.
` rArr p=q =r`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-SEQUENCES AND SERIES -EXERCISE 17
  1. If p,q,r are in G.P and tan^(-1)p,tan^(-1)q,tan^(-1)r are in A.P then ...

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