证明题求解，如图
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let
y=π/2-x
dy =-dx
x=0, y=π/2
x=π/2, y=0
I
=∫(0->π/2) dx/(1+(tanx))^2
=∫(π/2->0) -dy/(1+(coty))^2
=∫(0->π/2) dy/(1+(coty))^2
2I =∫(0->π/2) dx/(1+(tanx))^2 + ∫(0->π/2) dx/(1+(cotx))^2
=∫(0->π/2) dx
=π/2
I=π/4
y=π/2-x
dy =-dx
x=0, y=π/2
x=π/2, y=0
I
=∫(0->π/2) dx/(1+(tanx))^2
=∫(π/2->0) -dy/(1+(coty))^2
=∫(0->π/2) dy/(1+(coty))^2
2I =∫(0->π/2) dx/(1+(tanx))^2 + ∫(0->π/2) dx/(1+(cotx))^2
=∫(0->π/2) dx
=π/2
I=π/4
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