化简【2sin50°+sin10°(1+根号3tan10°)】乘根号下2(sin80°的平方)
来源:学生作业帮 编辑:搜搜做题作业网作业帮 分类:数学作业 时间:2024/05/04 18:11:44
化简【2sin50°+sin10°(1+根号3tan10°)】乘根号下2(sin80°的平方)
【2sin50+sin10(1+√3tan10)】*√(2(sin80)^2)
=【2sin50+sin10(1+√3Sin10/Cos10)】*√(2(sin80)^2)
=【2sin50+sin10(Cos10+√3Sin10)/Cos10)】*√(2(sin80)^2)
=【2sin50+2sin10(sin30Cos10+cos30Sin10)/Cos10)】*√(2(sin80)^2)
=【2sin50+2sin10sin40/Cos10)】*√(2(sin80)^2)
=2【(sin50Cos10+sin10sin40)/Cos10】*√(2(sin80)^2)
=2【sin60/Cos10】*√(2(sin80)^2)
=2sin60/Cos10*√2*cos10
=2sin60*√2
=根号6
=【2sin50+sin10(1+√3Sin10/Cos10)】*√(2(sin80)^2)
=【2sin50+sin10(Cos10+√3Sin10)/Cos10)】*√(2(sin80)^2)
=【2sin50+2sin10(sin30Cos10+cos30Sin10)/Cos10)】*√(2(sin80)^2)
=【2sin50+2sin10sin40/Cos10)】*√(2(sin80)^2)
=2【(sin50Cos10+sin10sin40)/Cos10】*√(2(sin80)^2)
=2【sin60/Cos10】*√(2(sin80)^2)
=2sin60/Cos10*√2*cos10
=2sin60*√2
=根号6
化简【2sin50°+sin10°(1+根号3tan10°)】乘根号下2(sin80°的平方)
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