1.求证:sinθ(1+tanθ)+cosθ(1+1/tanθ)=1/tanθ+1/cosθ 2.已知tana=-1/3,求(4sina-2cosa)/(5cosa+3sina) 3.化简:根号(1-2sin10°cos10°)/(sin10°-根号(1-sin²10°))=1/tanθ+1/cosθ 改为)=1/sinθ+1/cosθ
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![1.求证:sinθ(1+tanθ)+cosθ(1+1/tanθ)=1/tanθ+1/cosθ 2.已知tana=-1/3,求(4sina-2cosa)/(5cosa+3sina) 3.化简:根号(1-2sin10°cos10°)/(sin10°-根号(1-sin²10°))=1/tanθ+1/cosθ 改为)=1/sinθ+1/cosθ](/uploads/image/z/2093396-68-6.jpg?t=1.%E6%B1%82%E8%AF%81%3Asin%CE%B8%281%2Btan%CE%B8%29%2Bcos%CE%B8%281%2B1%2Ftan%CE%B8%29%3D1%2Ftan%CE%B8%2B1%2Fcos%CE%B8+2.%E5%B7%B2%E7%9F%A5tana%3D-1%2F3%2C%E6%B1%82%EF%BC%884sina-2cosa%29%2F%285cosa%2B3sina%29+3.%E5%8C%96%E7%AE%80%EF%BC%9A%E6%A0%B9%E5%8F%B7%EF%BC%881-2sin10%C2%B0cos10%C2%B0%EF%BC%89%2F%EF%BC%88sin10%C2%B0-%E6%A0%B9%E5%8F%B7%EF%BC%881-sin%26%23178%3B10%C2%B0%EF%BC%89%EF%BC%89%3D1%2Ftan%CE%B8%2B1%2Fcos%CE%B8+%E6%94%B9%E4%B8%BA%29%3D1%2Fsin%CE%B8%2B1%2Fcos%CE%B8)
1.求证:sinθ(1+tanθ)+cosθ(1+1/tanθ)=1/tanθ+1/cosθ 2.已知tana=-1/3,求(4sina-2cosa)/(5cosa+3sina) 3.化简:根号(1-2sin10°cos10°)/(sin10°-根号(1-sin²10°))=1/tanθ+1/cosθ 改为)=1/sinθ+1/cosθ
1.求证:sinθ(1+tanθ)+cosθ(1+1/tanθ)=1/tanθ+1/cosθ 2.已知tana=-1/3,求(4sina-2cosa)/(5cosa+3sina) 3.化简:根号(1-2sin10°cos10°)/(sin10°-根号(1-sin²10°))
=1/tanθ+1/cosθ 改为)=1/sinθ+1/cosθ
1.求证:sinθ(1+tanθ)+cosθ(1+1/tanθ)=1/tanθ+1/cosθ 2.已知tana=-1/3,求(4sina-2cosa)/(5cosa+3sina) 3.化简:根号(1-2sin10°cos10°)/(sin10°-根号(1-sin²10°))=1/tanθ+1/cosθ 改为)=1/sinθ+1/cosθ
sinθ(1+tanθ)+cosθ(1+1/tanθ)
=sinθ(1+sinθ/cosθ)+cosθ(1+cosθ/sinθ)
=sinθ(cosθ+sinθ)/cosθ+cosθ(sinθ+cosθ)/sinθ
=(sinθ+cosθ)(sinθ/cosθ+cosθ/sinθ)
=(sinθ+cosθ)(sin²θ+cos²θ)/(cosθsinθ)
=(sinθ+cosθ)/(cosθsinθ)
=1/sinθ+1/cosθ
2.∵tana=-1/3 ∴sina/cosa=-1/3
∴cosa=-3sina
∴(4sina-2cosa)/(5cosa+3sina)
=(4sina+6sina)/(-10sina+3sina)
=-10/7
3.化简:
√(1-2sin10°cos10°)/(sin10°-√(1-sin²10°))
=√(sin²10º+cos²10º-2sin10°cos10°)/sin10°-√cos²10°)
=√(cos10º-sin10º)/(sin10º-cos10º)
=|cos10º-sin10º|/(sin10º-cos10º)
=(cos10º-sin10º)/(sin10º-cos10º) (cos10º>sin10º)
=-1
∴tana=sina/cosa=-12/5
1、原式=sin(1+sin/cos)+cos(1+cos/sin)=sin+sin^2/cos+cos+cos^2/sin=(sin^2+cos^2)/cos+(sin^2+cos^2)/sin=1/sin+1/cos
2、tana=sina/cosa=-1/3,则sina=-cosa/3,则所求式子=(-4cosa/3-2cosa)/(5cosa-3cosa/3)=-5/6
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1、原式=sin(1+sin/cos)+cos(1+cos/sin)=sin+sin^2/cos+cos+cos^2/sin=(sin^2+cos^2)/cos+(sin^2+cos^2)/sin=1/sin+1/cos
2、tana=sina/cosa=-1/3,则sina=-cosa/3,则所求式子=(-4cosa/3-2cosa)/(5cosa-3cosa/3)=-5/6
3、原式=根号(sin^2+cos^2-2sincos)/(sin-根号(sin^2+cos^2-sin^2))=(cos-sin)/(sin-cos)=-1
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