cot1°*cot2°*cot3°....cot89°/(cot1°+cot2°+cot3°+...+cot89°)

很简单cot1°*cot89°=1,cot2°*cot88°=1
依次类推cot45°=1
所以分子=1
cot1°+cot89°
=cot1°+1/cot1°
=根号(cot1°+1/cot1°)^2
=根号{cot1°^2+1/cot1°^2+2}
=根号{cot1°^2+tan1°^2+2}
=根号{1+2}
=根号3
((cot1°+cot2°+cot3°+...+cot89°
=44乘以根号3 +cot45°
=44乘以根号3 +1
原式=1/44*根号3+1
=44乘以根号3-1/131