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Question

The value of limnπ6n[sec2(π6n)+sec2(2π6n)++sec2((n1)π6n)+43] is

A
33
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B
3
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C
2
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D
23
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Solution

The correct option is A 33
limnπ6n[sec2(π6n)+sec2(2π6n)++sec2((n1)π6n)+43]
=π6limn1nnr=1sec2(rπ6n)
=π610sec2(πx6) dx
=[tanπx6]10
=13=33

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