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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_(1) a_(2))) + tan^(-1) ((d)/(1 + a_(2) a_(3))) + ...+ tan^(-1) ((d)/(1 + a_( - 1)a_(n)))] = ((n -1)d)/(1 + a_(1) a_(n))`

A

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

B

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

C

`(nd)/(1+a_(1)a_(n))`

D

`(a_(n)+a_(1))/(a_(1)+a_(n))`

Text Solution

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The correct Answer is:
B
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