cos40°(1+√3tan10°)
=cos40°·[(cos10°+√3sin10°)/cos10°]
=cos40°[2(sin30°cos10°+cos30°sin10°)/cos10°]
=(2cos40°sin40°)/cos10°
=sin80°/cos10°
=cos10°/cos10°
=1.
cos40°(1+√3tan10°)
=cos40°·[(cos10°+√3sin10°)/cos10°]
=cos40°[2(sin30°cos10°+cos30°sin10°)/cos10°]
=(2cos40°sin40°)/cos10°
=sin80°/cos10°
=cos10°/cos10°
=1.