Question

sin50°（1+√3tan10°）的值 我解得自己也看不懂，请教下

Answer 1

度我省略了，打起来复杂
原式=sin50(1+tan10tan60)
=sin50(tan60-tan10)/tan50 .......（正切差角公式）
=cos50(3^0.5-tan10)
=cos50(3^0.5 cos10-sin10)/cos10
=cos50sec10 -2sin(10-60) ........（辅助角公式）
=2sin50cos50sec10
=sin100/cos10=1

Answer 2

sin50°(1+√3tan10°)
=sin50°(1+√3sin10°/cos10°)
=sin50°(cos10°+√3sin10°)/cos10°
=2sin50°sin(30°+10°)/cos10°
=2sin50°sin40°/cos10°
=2cos40°sin40°/cos10°
=sin80°/cos10°
=cos10°/cos10°
=1