(1-tan40°tan80°)/(cot50°+cot10°)的值为?

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(1-tan40°tan80°)/(cot50°+cot10°)的值为?
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(1-tan40°tan80°)/(cot50°+cot10°)的值为?
(1-tan40°tan80°)/(cot50°+cot10°)的值为?

(1-tan40°tan80°)/(cot50°+cot10°)的值为?
(1-tan40°tan80°)/(cot50°+cot10°)
=(cos40cos80-sin40sin80)/cos40cos80/((cos50sin10+sin50cos10)/sin50sin10)
=cos(40+80)/sin(50+10)
=-cos60/sin60
=-√3/3

=(1-sin40sin80/cos40cos80)/(cos50/sin50+cos10/sin10)
=[(cos40cos80-sin40sin80)/cos40cos80]/[(sin10cos50+cos10sin50)/sin50sin10]
=[cos(80+40)/sin50sin10]/[sin(10+50)]/sin50sin10]
=cos120/sin60
=-√3/3