求值:2sin50°+cos10°*(1+根号3tan10°)/cs35°cos40°+cos50°cos55°是cos35° 不好意思。打错了
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/05 17:27:09
![求值:2sin50°+cos10°*(1+根号3tan10°)/cs35°cos40°+cos50°cos55°是cos35° 不好意思。打错了](/uploads/image/z/4522903-7-3.jpg?t=%E6%B1%82%E5%80%BC%3A2sin50%C2%B0%2Bcos10%C2%B0%2A%EF%BC%881%2B%E6%A0%B9%E5%8F%B73tan10%C2%B0%EF%BC%89%2Fcs35%C2%B0cos40%C2%B0%2Bcos50%C2%B0cos55%C2%B0%E6%98%AFcos35%C2%B0+%E4%B8%8D%E5%A5%BD%E6%84%8F%E6%80%9D%E3%80%82%E6%89%93%E9%94%99%E4%BA%86)
求值:2sin50°+cos10°*(1+根号3tan10°)/cs35°cos40°+cos50°cos55°是cos35° 不好意思。打错了
求值:2sin50°+cos10°*(1+根号3tan10°)/cs35°cos40°+cos50°cos55°
是cos35° 不好意思。打错了
求值:2sin50°+cos10°*(1+根号3tan10°)/cs35°cos40°+cos50°cos55°是cos35° 不好意思。打错了
原式的分子部分=2sin50° + cos10° + √3cos10°×[(sin10°)/(cos10°)]
=2sin50° + cos10° + √3sin10°
=2sin50° + 2[(1/2)cos10° + (√3/2)sin10°]
=2sin50° + 2sin(10°+ 30°)
=2sin50° + 2sin40°
=2sin[(50°+40°)/2]cos[(50°-40°)/2]
=2sin45°×cos5°
=√2cos5°
原式的分母部分=(1/2)[cos(35°+40°) + cos(35°-40°)] + (1/2)[cos(50°+55°) + cos(50°-55°)]
=(1/2)[cos75° + cos(-5°)] + (1/2)[cos105° + cos(-5°)]
=(1/2)cos75° + (1/2)cos5° + (1/2)cos105° + (1/2)cos5°
=(1/2)(cos75° + cos105°) + cos5°
=(1/2){2cos[(75°+105°)/2]cos[(75°-105°)/2]} + cos5°
=cos90°cos(-15°) + cos5°
=cos5°
整理后得:=(√2cos5°)/(cos5°) =√2