sin50*(1+√3*tan 10)

sin50°(1+√3*tan 10°)
=(sin50°cos10°+√3sin50°sin10°)/cos10°
=[sin(60°-10°)cos10°+√3sin(60°-10°)sin10°]/cos10°
=(sin60°cos10°^2-cos60°sin10°cos10°+√3sin60°cos10°sin10°-√3cos60°sin10°^2)/cos10°
=[√3/2*(cos10°^2-sin10°^2)+sin10°cos10°]/cos10°
=(√3/2*cos20°+1/2*sin20°)/cos10°
=(sin60°cos20°+cos60°sin20°)/cos10°
=sin80°/cos10°
=1
一般这类题目都可以把切化玄做
虽然不一定最简单 但一定做得出

sin50*(1+√3*tan 10)
=2sin50*(1/2+√3/2*sin10/cos10)
=2sin50 * (sin30*cos10+cos30*sin10)/cos10
=2sin50*sin40/cos10
=2cos40*sin40/cos10
=sin80/cos10
=1