高中数学化简题sin50°(1+根号3)=
1个回答

是这二个吗?

sin50°(1+√3×cot80°)

=sin50[sin80+√3×cos80]/sin80

=2sin50{(1/2)cos80+(√3/2)sin80}/sin80

=2sin50cos50/sin80

=sin100/sin80

=sin80/sin80

=1

sin50°[1+(√3)×tan10°]

=sin50×[(√3)sin10+cos10]/cos10

=(sin50/cos10)×2×(cos30sin10+cos10sin30)

=(sin50/cos10)×2×sin40

=2×sin50×cos50/cos10

=sin100/cos10

=cos10/cos10

=1