sin50°(1+根号3tan10°)等于多少

网友回答

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======以下答案可供参考======
供参考答案1:
1供参考答案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供参考答案3:
解法一：sin50°（1+√3tan10°）
=2sin50°[1/2+(√3/2)sin10°/cos10°]
=2sin50°[1/2cos10°+(√3/2)sin10°]/cos10°
=2sin50°[cos60°cos10°+sin60°sin10°]/cos10°
=2sin50°cos(60°-10°) /cos10°
=2sin50°cos50° /cos10°
=sin100°/cos10°
=cos10°/cos10°
=1解法二：sin50(1+√3*tan10)
= sin50(1 + √3 sin10/cos10)
= (sin50/cos10)(cos10 + √3sin10)
= 2(sin50/cos10)(sin30cos10 + cos30sin10)
= 2(sin50/cos10)sin(30+10)
= 2sin50*sin40/cos10
= 2sin50*cos50/cos10= sin100/cos10= sin80/cos10= sin80/sin80= 1