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Question

If tan12mm4+m2+2=am, then a1+a2+a3+.........to =

A
π4
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B
π4
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C
3π4
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D
None
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Solution

The correct option is A π4
tan12m2+m2+m4=tan12m1+(m4+m2+1)=tan1(m2+m+1)(m2m+1)1+(m2+m+1)(m2m+1)=tan1(m2+m+1)tan1(m2m+1)
Let Sn=nm=1tan12m2+m2+m4=(tan13=tan11)+(tan17tan13)+(tan13tan17)+......+tan1(n2+n+1)tan1(n2n+1)=tan1(n2+n+1)tan11
As n,tan2(n2+n+1)π2
as n2+n+1
Hence S=π2π4=π4.

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