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If `a_1, a_2,a_3, ,a_n` is an A.P. with common difference `d ,` then prove that `"tan"[tan^(-1)(d/(1+a_1a_2))+tan^(-1)(d/(1+a_2a_3))+tan^(-1)(d/(11+a_(n-1)a_n))]=((n-1)d)/(1+a_1a_n)`

A

`tan^(-1)""(nd)/(1+a_(1)a_(n+1))`

B

`tan^(-1)""((n+1)d)/(1+a_(1)a_(n+1))`

C

`tan^(-1)""((n+1)d)/(1+a_(1)a_(n+1))`

D

`tan^(-1)""((n+1)nd)/(1+a_(1)a_(n+1))`

Text Solution

Verified by Experts

The correct Answer is:
A
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