化简:[2sin50°+sin10°*(1+√3 tan 10°)]√2sin^2 80°

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/04 10:59:07
化简:[2sin50°+sin10°*(1+√3 tan 10°)]√2sin^2 80°

化简:[2sin50°+sin10°*(1+√3 tan 10°)]√2sin^2 80°
化简:[2sin50°+sin10°*(1+√3 tan 10°)]√2sin^2 80°

化简:[2sin50°+sin10°*(1+√3 tan 10°)]√2sin^2 80°
∵cos10+√3sin10
=2[(1/2)cos10+(√3/2)sin10]
=2(cos60cos10+sin60sin10)
=2cos(60-10)
=2cos50
∴{2sin50+[1+(√3)tan10]sin10}×√[2(sin80)^]
={2sin50+[1+(√3)(sin10/cos10)]sin10}×√[2(sin80)^]
={2sin50+[1+(√3)(sin10/cos10)]sin10}×√[2(sin80)^]
={2sin50+[cos10+(√3)(sin10)]sin10/cos10}×√[2(sin80)^]
=[2sin50+(2cos50sin10/cos10)]×(√2)(sin80)
=2[(cos10sin50+cos50sin10)/cos10]×(√2)cos10
=2(sin60/cos10)×(√2)(sin80)
=(2√2)×(√3)/2=√6