2sin50°+cos10°(1+√3tan10°)/cos35°cos40°+cos50°cos55°怎么化简.

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/03 07:12:18

2sin50°+cos10°(1+√3tan10°)/cos35°cos40°+cos50°cos55°怎么化简.
2sin50°+cos10°(1+√3tan10°)/cos35°cos40°+cos50°cos55°怎么化简.

2sin50°+cos10°(1+√3tan10°)/cos35°cos40°+cos50°cos55°怎么化简.
原式=2sin50°+cos10°+√3sin10°/cos35°cos40°+sin(90-50)°sin(90-55)°
=2sin50°+2(cos60°cos10°+sin60°sin10°)/cos(40-35)°
=2sin50°+2cos50°/cos5°
=2√2(cos45°cos50°+sin45°sin50°)/cos5°
=2√2cos(50-45)°/cos5°
=2√2