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Evaluate : int(pi/3)^(pi/4)(tanx+cotx)^...

Evaluate : `int_(pi/3)^(pi/4)(tanx+cotx)^2dx`

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Given,I= `int_(pi/3)^(pi/4)(tanx+cotx)^2dx`
=`int_(pi/3)^(pi/4)(tan^2x+cot^2x+2tanxcotx)^2dx`
I=`int_(pi/3)^(pi/4)(sec^2x-1+cosec^2x-1+2)^2dx`
I=`int_(pi/3)^(pi/4)(sec^2x+cosec^2x)^2dx`
I=`[tanx-cotx]_(pi/3)^(pi/4)`
I=`-2/sqrt(3)`
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