Question

化简Sin50度(1+根号3tan10度)

Answer 1

你好，这是一道3角还原的题，有一定难度，不过有固定方法的，
题中1+√3tan10=(cos10+√3sin10)/cos10=2(1/2cos10+√3/2sin10)/cos10=
2(cos60cos10+sin60sin10)/cos10=2cos50/cos10
代入原题中sin50*2cos50/cos10=2sin50*cos50/cos10=sin100/cos10=cos(-10)/cos10=cos10/cos10=1
望采纳

Answer 2

sin50（1+√3tan10）
=sin50[1+√3(sin10/cos10)]
=sin50[(cos10+√3sin10)/cos10]
=sin50[2sin(30+10)/cos10]
=(2sin50sin40)/cos10°
=(2cos40°*sin40°)/cos10°
=sin80°/cos10°
=cos10°/cos10°
=1

Answer 3

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