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Question

The area between the curves y=tan x, cot x and axis in the interval [0,π/2]is ?

A
log 2
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B
log 3
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C
log 5
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D
none of these
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Solution

The correct option is A log 2
y=tanx,y=cotx are symmetrical about x=π4,where they intersect

π4ReqArea=2|tanxdx|

π4|2cotxdx|=2×(lnsecπ4)lnsec0

π22×|ln20|=2×12×ln2=ln2

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