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Question

If In=π/40 tann x dx, then the value of I9+I11 is

A
19
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B
110
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C
111
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D
18
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Solution

The correct option is B 110
We have,
In=π/40 tann x dxIn+2=π/40 tann+2 x dxIn+2+In=π/40 tann+2 x dx+π/40 tann x dxIn+2+In=π/40( tann+2 x+ tann x) dxIn+2+In=π/40 tann x( tan2 x+1) dxIn+2+In=π/40 tann xsec2 x dxLet tan x=tsec2 x dx=dtAlso, x=0t=0 and x=π4t=1In+2+In=10tn dt=(tn+1n+1]10=1n+1I9+I11=110

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