化简（1+cos20)/2sin20-sin10(cot5-tan5)答案等于根3/2看着简单化简起来难.......

Question

化简 （1+cos20)/2sin20 -sin10(cot5-tan5) 答案等于根3/2
看着简单化简起来难.......

Answer 1

（1+cos20)/2sin20 -sin10(cot5-tan5)
=[1+ 2 (cos10)^2-1]/4sin10 cos10 - 2sin5 cos 5 (cos5/sin5 - sin5/cos5)
=cos10/2sin10 - 2[(cos5)^2 - (sin5)^2]
=cos10/2sin10- 2 cos10
=(cot10 -4 cos10)/2
=(cos10-4sin10 cos10)/2sin10
=(sin80-2sin20)/2sin10
=(sin80-sin20-sin20)/2sin10
=(2cos50sin30 -sin20)/2sin10
=(cos50 - sin 20)/2sin10
=(sin40 - sin20)/2sin10
=2cos30sin10/2sin10
=cos30
=根3/2