1.化简sin²α+cosαcos(π/3+α)-sin²(π/6-α)2.求值:[sin50°(1+√3tan10°)-cos20°]/cos80°√1-cos20°第一个根号里面只有3,第二个根号里面是1-cos20°
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![1.化简sin²α+cosαcos(π/3+α)-sin²(π/6-α)2.求值:[sin50°(1+√3tan10°)-cos20°]/cos80°√1-cos20°第一个根号里面只有3,第二个根号里面是1-cos20°](/uploads/image/z/2757969-9-9.jpg?t=1.%E5%8C%96%E7%AE%80sin%26sup2%3B%CE%B1%2Bcos%CE%B1cos%28%CF%80%2F3%2B%CE%B1%29-sin%26sup2%3B%28%CF%80%2F6-%CE%B1%292.%E6%B1%82%E5%80%BC%EF%BC%9A%5Bsin50%C2%B0%EF%BC%881%2B%E2%88%9A3tan10%C2%B0%EF%BC%89-cos20%C2%B0%5D%2Fcos80%C2%B0%E2%88%9A1-cos20%C2%B0%E7%AC%AC%E4%B8%80%E4%B8%AA%E6%A0%B9%E5%8F%B7%E9%87%8C%E9%9D%A2%E5%8F%AA%E6%9C%893%2C%E7%AC%AC%E4%BA%8C%E4%B8%AA%E6%A0%B9%E5%8F%B7%E9%87%8C%E9%9D%A2%E6%98%AF1-cos20%C2%B0)
1.化简sin²α+cosαcos(π/3+α)-sin²(π/6-α)2.求值:[sin50°(1+√3tan10°)-cos20°]/cos80°√1-cos20°第一个根号里面只有3,第二个根号里面是1-cos20°
1.化简sin²α+cosαcos(π/3+α)-sin²(π/6-α)
2.求值:[sin50°(1+√3tan10°)-cos20°]/cos80°√1-cos20°
第一个根号里面只有3,第二个根号里面是1-cos20°
1.化简sin²α+cosαcos(π/3+α)-sin²(π/6-α)2.求值:[sin50°(1+√3tan10°)-cos20°]/cos80°√1-cos20°第一个根号里面只有3,第二个根号里面是1-cos20°
1
sin²α+cosαcos(π/3+α)-sin²(π/6-α)
=sin²α+cosα(cosπ/3cosα-sinπ/3sina)-(sinπ/6cosα-cosπ/6sina)²
=sin²α+cosα(1/2cosα-√3/2sina)-(1/2cosa-√3/2sina)²
=sin²α+(1/2cosα-√3/2sina)(cosa-1/2cosa+3/2sina)
=sin²α+1/4cos²a-3/4son²a=1/4
2
sin50°(1+√3tan10°)-cos20°
=cos10°(sin50°(1+√3tan10°)-cos20°)/cos10°
=(sin50(cos10+√3sin10)-cos20cos10)/cos10
=(2sin50(1/2cos10+√3/2sin10)-cos20cos10)/cos10
=(2sin50cos(60-10)-cos20cos10)/cos10
=(2sin50cos(50)-cos20cos10)/cos10
=(sin100-cos20cos10)/cos10
=(cos10-cos20cos10)/cos10=1-cos20
所以原式=(1-cos20)/cos80°√1-cos20°=√(1-cos20)/cos80°
==√(1-(1-2sin10^2))/cos80°=根号2sin10/cos80=根号2
1.化简sin²α+cosαcos(π/3+α)-sin²(π/6-α)
=sin²α+cosα(cosπ/3cosα-sinπ/3sina)-(sinπ/6cosα-cosπ/6sina)²
=sin²α+cosα(1/2cosα-√3/2sina)-(1/2cosa-√3/2sina)²
=sin²α...
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1.化简sin²α+cosαcos(π/3+α)-sin²(π/6-α)
=sin²α+cosα(cosπ/3cosα-sinπ/3sina)-(sinπ/6cosα-cosπ/6sina)²
=sin²α+cosα(1/2cosα-√3/2sina)-(1/2cosa-√3/2sina)²
=sin²α+(1/2cosα-√3/2sina)(cosa-1/2cosa+3/2sina)
=sin²α+1/4cos²a-3/4son²a=1/4
.求值:[sin50°(1+√3tan10°)-cos20°]/ cos80°√1-cos20
=
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