四道三角函数的题,1.用cosα表示(sinα)^4-(sinα)^2+(cosα)^22.化简:(根号下(1-2sin10°cos10°))/(cos10°-根号下(1-(cos170°)^2)3.α在第二象限,化简cosα根号下[(1-sinα)/(1+sinα)]+sinα根号下[(1-cosα)/(1+cosα)]4.化简[

四道三角函数的题,1.用cosα表示(sinα)^4-(sinα)^2+(cosα)^22.化简:(根号下(1-2sin10°cos10°))/(cos10°-根号下(1-(cos170°)^2)3.α在第二象限,化简cosα根号下[(1-sinα)/(1+sinα)]+sinα根号下[(1-cosα)/(1+cosα)]4.化简[
四道三角函数的题,
1.用cosα表示(sinα)^4-(sinα)^2+(cosα)^2
2.化简:(根号下(1-2sin10°cos10°))/(cos10°-根号下(1-(cos170°)^2)
3.α在第二象限,化简cosα根号下[(1-sinα)/(1+sinα)]+sinα根号下[(1-cosα)/(1+cosα)]
4.化简[1-(sinx)^6-(cosx)^6]/[1-(sinx)^4-(cosx)^4]
嗯,有点多呃,

四道三角函数的题,1.用cosα表示(sinα)^4-(sinα)^2+(cosα)^22.化简:(根号下(1-2sin10°cos10°))/(cos10°-根号下(1-(cos170°)^2)3.α在第二象限,化简cosα根号下[(1-sinα)/(1+sinα)]+sinα根号下[(1-cosα)/(1+cosα)]4.化简[
(一)
(sinα)^4-(sinα)^2+(cosα)^2
=(1-cosα^2)^2-(1-cosα^2)+(cosα)^2
=1-2cosα^2+cosα^4-1+cosα^2+cosα^2
=cosα^4
(二)化简分子
=√[sin^2(10°)+cos^2(10°)-2sin10°cos10°]
＝√(sin10°-cos10°)^2=sin10°-cos10°;
化简分母
=cos10°-√[1-cos^2(180°-10°)]
=cos10°-√[1-cos^2(10°)]
=cos10°-sin10°
原式＝（sin10°-cos10°）/(cos10°-sin10°)=-1
(三)第一项化简
=cosα√{[(1-sinα)(1-sinα)]/[(1+sinα)(1-sinα)]}
=cosα√[(1-sinα)^2]/[1-sin^2(α)]
=cosα√[(1-sinα)^2]/cos^2(α)
=cos(1-sinα)/(-cosα) =sinα-1
因为α在第二象限,所以cosα是负数.开方出来要加负号.
第二项化简
=sinα√{[(1-cosα)(1-cosα)]/[(1+cosα)(1-cosα)]}
=sinα√[(1-cosα)^2]/[1-cos^2(α)]
=sinα√[(1-cosα)^2]/sin^2(α)
=sinα(1-cosα)/sinα =1-cosα
所以原式＝sinα-1+1-cosα＝sinα-cosα
(四)化简分子
＝(sinx)^2+(cosx)^2-(sinx)^4(sinx)^2-(cosx)^4(cosx)^2
＝(sinx)^2[1-(sinx)^4]+(cosx)^2[1-(cosx)^4]
＝(sinx)^2{[1+(sinx)^2][1-(sinx)^2]}+(cosx)^2{[(1+(cosx)^2)][(1-(cosx)^2]}
＝(sinx)^2[1+(sinx)^2](cosx)^2+(cosx)^2{[(1+(cosx)^2)](sinx)^2
＝(sinx)^2(cosx)^2{1+(sin)^2+1+(cosx)^2)}
=3(sinx)^2(cosx)^2
化简分母
＝(sinx)^2+(cosx)^2-(sinx)^2(sinx)^2-(cosx)^2(cosx)^2
＝(sinx)^2[1-(sinx)^2]+(cosx)^2[1-(cosx)^2]
＝(sinx)^2(cosx)^2+(cosx)^2(sinx)^2
＝2(sinx)^2(cosx)^2
原式＝[3(sinx)^2(cosx)^2]/[2(sinx)^2(cosx)^2]＝3/2

1.(1-cosα)^2-(1-cosα)+(cosα)^2

1.(cos(a))^4-1
2.1
3.sin^2(a)-cos^2(a)
4.3/2
就是抓住sin^2(x)+cos^2(x)=1,和四个象限角的大小关系求解
尤其是第四个要多次运用这个公式

1: (sinα)^4-(sinα)^2+(cosα)^2
=(sinα)^4-(sinα)^2+1-(sinα)^2
=(sinα)^4-2(sinα)^2+1
=[(sinα)^2-1]^2
=[1-(sinα)^2]^2
=(cosα)^4
2: :(根号下(1-2sin10°cos10°))/(cos10°-根号下(1-(cos170°)^2)
=(sin10°-cos10°)^2/(cos10°-sin10°)
=1

(sinα)^4-(sinα)^2+(cosα)^2
=[(sinα)^2]^2-[1-(cosα)^2]+(cosα)^2
=[1-(cosα)^2]^2-1+2(cosα)^2
=(cosα)^4-2(cosα)^2+1-1+2(cosα)^2
=(cosα)^4
(根号下(1-2sin10°cos10°))/(cos10°-根号下(1-(cos170...

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(sinα)^4-(sinα)^2+(cosα)^2
=[(sinα)^2]^2-[1-(cosα)^2]+(cosα)^2
=[1-(cosα)^2]^2-1+2(cosα)^2
=(cosα)^4-2(cosα)^2+1-1+2(cosα)^2
=(cosα)^4
(根号下(1-2sin10°cos10°))/(cos10°-根号下(1-(cos170°)^2)
={根号下[(sin10)^2+(cos10)^2-2sin10cos10]}/[cos10-根号下(sin170)^2]
=[根号下(sin10-cos10)^2]/(cos10-sin170)
=(cos10-sin10)/(cos10-sin10)
=1
cosα根号下[(1-sinα)/(1+sinα)]+sinα根号下[(1-cosα)/(1+cosα)]
=cosα根号下[(1-sinα)(1-sinα)/(1+sinα)(1-sinα)]+sinα根号下[(1-cosα)(1-cosα)/(1+cosα)(1-cosα)]
=cosα根号下[(1-sinα)^2/(cosα)^2]+sinα根号下[(1-cosα)^2/(sinα)^2]
=cosα(1-sinα)/(-cosα)+sinα(1-cosα)/(sinα)
=sinα-1+1-cosα
=sinα-cosα
[1-(sinx)^6-(cosx)^6]/[1-(sinx)^4-(cosx)^4]
=[(sinx)^2+(cosx)^2-(sinx)^6-(cosx)^6]/[(sinx)^2+(cosx)^2-(sinx)^4-(cosx)^4]
=[(sinx)^2(1-(sinx)^4)+(cosx)^2(1-(cosx)^4)]/[(sinx)^2(1-(sinx)^2)+(cosx)^2(1-(cosx)^2)]
=[(sinx)^2(1-(sinx)^2)(1+(sinx)^2)+(cosx)^2(1-(cosx)^2)(1+(cosx)^2)/[(sinx)^2(cosx)^2+(cosx)^2(sinx)^2]
=[(sinx)^2(cosx)^2(1+(sinx)^2)+(sinx)^2(cosx)^2(1+(cosx)^2)]/[2(sinx)^2(cosx)^2]
=3(sinx)^2(cosx)^2/[2(sinx)^2(cosx)^2]
=3/2

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都比较简单 但是 我都不会