题目

求值:2sin50°+cos10°*（1+根号3tan10°）/cs35°cos40°+cos50°cos55°
是cos35° 不好意思。打错了

提问时间：2020-11-05

答案

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