вычислите 1-√3ctg40+1/cos20
40 и 20 в градусах

1 -√3*ctq40°+1/cos20° =1 -√3scos40°/sin40° +1/cos20° =
((sin40°-√3cos40°) +2sin20°)/sin40°=(2sin(40° - 60°)+2sin20° )/sin40°=
(2sin(-20°) +2sin20°)/sin40° = (-2sin20° +2sin20°)/sin40° =0/sin40° =0.
 
* * *  sin40°-√3cos40° =2((1/2)*sin40°-(√3/2)*cos40°)
 =2(cos60°*sin40°-sin60°cos40°) =2sin(40° -60°) =2sin(-20°) = -2sin20°  * *  *