1.化简:(1-sin^6α -cos^6α)/(1-sin^4α -cos^4α)2.α为三角形内角,lg(sinα + cosα)=1/2lg5 -lg3,求sinα - cosα,tanα的值.3.已知:log(tanα)(cosα)=2/3 (0<α<π/2),求证:log(1+cot^2α)(sinα*cosα)=-7/10.4.已知:5sinβ=sin(
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![1.化简:(1-sin^6α -cos^6α)/(1-sin^4α -cos^4α)2.α为三角形内角,lg(sinα + cosα)=1/2lg5 -lg3,求sinα - cosα,tanα的值.3.已知:log(tanα)(cosα)=2/3 (0<α<π/2),求证:log(1+cot^2α)(sinα*cosα)=-7/10.4.已知:5sinβ=sin(](/uploads/image/z/13447069-61-9.jpg?t=1.%E5%8C%96%E7%AE%80%EF%BC%9A%EF%BC%881-sin%5E6%CE%B1+-cos%5E6%CE%B1%29%2F%281-sin%5E4%CE%B1+-cos%5E4%CE%B1%292.%CE%B1%E4%B8%BA%E4%B8%89%E8%A7%92%E5%BD%A2%E5%86%85%E8%A7%92%2Clg%28sin%CE%B1+%2B+cos%CE%B1%29%3D1%2F2lg5+-lg3%2C%E6%B1%82sin%CE%B1+-+cos%CE%B1%2Ctan%CE%B1%E7%9A%84%E5%80%BC.3.%E5%B7%B2%E7%9F%A5%EF%BC%9Alog%28tan%CE%B1%29%28cos%CE%B1%29%3D2%2F3+%280%EF%BC%9C%CE%B1%EF%BC%9C%CF%80%2F2%29%2C%E6%B1%82%E8%AF%81%3Alog%281%2Bcot%5E2%CE%B1%29%28sin%CE%B1%2Acos%CE%B1%29%3D-7%2F10.4.%E5%B7%B2%E7%9F%A5%EF%BC%9A5sin%CE%B2%3Dsin%EF%BC%88)
1.化简:(1-sin^6α -cos^6α)/(1-sin^4α -cos^4α)2.α为三角形内角,lg(sinα + cosα)=1/2lg5 -lg3,求sinα - cosα,tanα的值.3.已知:log(tanα)(cosα)=2/3 (0<α<π/2),求证:log(1+cot^2α)(sinα*cosα)=-7/10.4.已知:5sinβ=sin(
1.化简:(1-sin^6α -cos^6α)/(1-sin^4α -cos^4α)
2.α为三角形内角,lg(sinα + cosα)=1/2lg5 -lg3,求sinα - cosα,tanα的值.
3.已知:log(tanα)(cosα)=2/3 (0<α<π/2),求证:log(1+cot^2α)(sinα*cosα)=-7/10.
4.已知:5sinβ=sin(2α+β) ,求tan(α+β)*cotα 的值.
1.化简:(1-sin^6α -cos^6α)/(1-sin^4α -cos^4α)2.α为三角形内角,lg(sinα + cosα)=1/2lg5 -lg3,求sinα - cosα,tanα的值.3.已知:log(tanα)(cosα)=2/3 (0<α<π/2),求证:log(1+cot^2α)(sinα*cosα)=-7/10.4.已知:5sinβ=sin(
零分?
①1-sin^6α -cos^6α
=1-(sin^2α+cos^2α)[(sin^2α+cos^2α)^2-3sin^2α*cos^2α))
=3sin^2α*cos^2α
1-sin^4α -cos^4α=1-[(sin^2α+cos^2α)^2-2sin^2α*cos^2α]
=2sin^2α*cos^2α
原式=3/2
②lg[(sinα + cosα)^2]=lg5 -lg9=lg5/9
(sinα + cosα)^2=5/9=1+2sinαcosα
2sinαcosα=-4/9
1-2sinαcosα=(sinα - cosα)^2=13/9
sinα - cosα=±√13/3
sinα + cosα=√5/3
2sinα=√5/3±√13/3负数去掉
sinα=(√5+√13)/6
cosα=(√5-√13)/6
tanα=(√5+√13)/(√5-√13)=-(9+√65)/3
③看不懂log(tanα)(cosα)=2/3=log[(tanα)(cosα)]?
log(tanα)(cosα)=2/3=log(sinα)=2/3
sin^2α=(10)^4/3=10*10^(1/3)
cos^2α=1- (10)^4/3
log(1+cot^2α)(sinα*cosα)=-log(sin^3αcosα)
④α+β=θ,
5sin(θ-α)=sin(θ+α)
4sinθcosα=6cosθsinα
tan(α+β)*cotα =tanθcotα=2/3