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If a1,a2,a3,…….an is an AP with common d...

If `a_1,a_2,a_3,…….a_n` is an AP with common difference d then `tan[tan^(-1)(d/(1+a_1a_2))+tan^(-1)((d)/(1+a_2a_3))+...+tan^(-1)((d)/(1+a_(n-1)a_n))]` is equal to a)`((n-1)d)/(a_1+a_n)` b)`((n-1)d)/(1+a_1a_n)` c)`(nd)/(1+a_1a_n)` d)`(a_n-a_1)/(a_n+a_1)`

A

`((n-1)d)/(a_1+a_n)`

B

`((n-1)d)/(1+a_1a_n)`

C

`(nd)/(1+a_1a_n)`

D

`(a_n-a_1)/(a_n+a_1)`

Text Solution

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The correct Answer is:
B
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