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Question

The sum to 'n' terms of the series
tan1(12)+tan1(29)+tan1(18)+tan1(225)+tan1(118)+..... terms


A

tan13

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B

cot1(13)

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C

tan1(13)

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D

None of these

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Solution

The correct options are
A

tan13


B

cot1(13)


Tr=tan1(2r+1)2

Sn=nr=1tan1(2r2+2r+1)

=tan1r+2r1+r(r+2)=tan1(r+2)tan1r

S=tan12tan11

S=tan1(3)=cot1(13)


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