sin50º(1+√3tan10º)的值

sin50º(1+√3tan10º)的值
sin50º(1+√3tan10º)的值

sin50º(1+√3tan10º)的值
tan50=tan(60-10)
=(tan60-tan10)/(1+tan60tan10)
原式=sin50(1+tan60tan10)
=sn50*(tan60-tan10)/tan50
=sin50/(sin50/cos50)*(sin60/cos60-sin10/cos10)
=cos50*(sin60cos10-cos60sin10)/(cos60cos10)
=cos50*sin50/(1/2*cos10)
=2sin50cos50/cos10
=sin100/cos10
=cos10/cos10
=1

1+√3tan10°
=1+√3sin10°/cos10°
=(cos10°+√3sin10°)/cos10°
=2sin(10°+30°)/cos10°
=2sin40°/cos10°
sin50°(1+√3tan10°)
=(2sin40°sin50°)/cos10°
=[cos(50°-40°)-cos(50°+40°)]/cos10°
=cos10°/cos10°
=1