Question

sin50°（1+根号3tan10°） 要过程~

1.sin40°（tan10°-根号3）
2. sin10°分之1-cos10°分之根号3
3. tan70°cos10°（根号3tan20°-1）
4. sin50°（1+根号3tan10°）

Answer 1

sin50°（1+根号3tan10°）
=sin50 / cos 10 * 2(1/2cos10+根号3 /2 sin10 )
= sin50 / cos10 * 2 cos50
=2 sin100 / cos10
=2

Answer 2

sin50(1+√3tan10)
=sin50[1+(√3sin10/cos10)]
=sin50[cos10+√3sin10)/cos10]
=2sin50[(1/2)cos10+(√3/2)sin10)/cos10]
=2sin50[cos60cos10+sin60sin10)/cos10]
=2sin50cos(60-10)/cos10
=2sin50cos50/cos10
=sin100/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