若sin(a)+sin(a)的平方=1 求cos(a)的平方 +cos(a)的六次方的值
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若sin(a)+sin(a)的平方=1 求cos(a)的平方 +cos(a)的六次方的值
若sin(a)+sin(a)的平方=1 求cos(a)的平方 +cos(a)的六次方的值
若sin(a)+sin(a)的平方=1 求cos(a)的平方 +cos(a)的六次方的值
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由题设可知:
sina+sin²a=1
sin²a+cos²a=1
∴sina=cos²a.
∴(cosa)^6=(cos²a)³
=sin³a
∴原式=cos²a+(cosa)^6
=sina+sin³a
=sina+sina(sin²a)
=sina+sina(1-sina)
=2sina-sin²a
=2sina-(1-sina)
=3sina-1
由题设可解得:sin²a+sina-1=0
sina=(-1+√5)/2
∴原式=(-5+3√5)/2
∵sina+sin²a=1=sin²a+cos²a
∴sina=cos²a
∵sina+sin²a=1
∴sina=1-sin²a
又∵sina∈[-1,1]
∴sina=(√5-1)/2
∴cos²a([cos²a]²+1)=cos²a(sin²a+1)=1-(sin²a)²=(1-sin²a)(1+sin²a)=[(-1+√5)/2][(5-√5)/2]=(3√5-5)/2
sina+sin^2a=1
sin^2a=1-sina
sina+sin^2a=1
sina=1-sin^2a
sina=cos^2a
sina=1-sin^2a
同时乘以sina
sin^2a=sina-sin^3a
∴sin^3a=sina-sin^2a
=cos^2a-sin^2a
=cos2a
∴sin...
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sina+sin^2a=1
sin^2a=1-sina
sina+sin^2a=1
sina=1-sin^2a
sina=cos^2a
sina=1-sin^2a
同时乘以sina
sin^2a=sina-sin^3a
∴sin^3a=sina-sin^2a
=cos^2a-sin^2a
=cos2a
∴sinθ+sin^2θ+sin^3θ
=cos^2a+sin^2θ+sin^3θ
=1+sin^3θ
=1+cos2θ
=2cos^2θ
=2sinθ
sina+sin^2a=1
sin^2a+sina-1=0
sin^2a+sina+1/4-1-1/4=0
(sina+1/2)^2-5/4=0
(sina+1/2-√5/2)(sina+1/2+√5/2)=0
sina=-1/2+√5/2或sina=-1/2-√5/2(舍去,-1<=sina<=1,-1/2-√5/2<-1)
cos^2a+cos^6a
=sina+(cos^2a)^3
=sina+sin^3a
=sina+sina-sin^2a
=2sina-(1-sina)
=2sina-1+sina
=3sina-1
=3*(-1/2+√5/2)-1
=-3/2+3√5/2-1
=-5/2+3√5/2
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若sin(a)+sin(a)的平方=1
sin²a=1-sina (1)
则sina=1-sin²a=cos²a (2)
又由sin²a+sina-1=0
sina=(-1+√5)/2 (负根小于-1舍去)
所以cos(a)...
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若sin(a)+sin(a)的平方=1
sin²a=1-sina (1)
则sina=1-sin²a=cos²a (2)
又由sin²a+sina-1=0
sina=(-1+√5)/2 (负根小于-1舍去)
所以cos(a)的平方 +cos(a)的六次方
=sina+(sina)³
=sina+sina*(1-sina)
=sina+sina-sin²a
=2sina-(1-sina)
=3sina-1
=3(-1+√5)/2-1
=(1/2)(-5+3√5)
收起
sin(a)+sin(a)的平方=1,所以sin(a)=1-sin(a)的平方=cos(a)平方,
因为sin(a)平方+cos(a)平方=1,所以sin(a)平方+sin(a)=1,
所以,cos(a)的平方 +cos(a)的六次方=cos(a)平方[1+cos(a)平方]=sin(a)(1+sin(a))=sin(a)+sin(a)平方=1
∵sinα+sinα=⒈又sinα+cosα=⒈
∴cosα=sinα
于是cosα+cos(a)的六次方=sinα+sinα
=sinα(1+sinα)=3sinα-1
由sinα+sinα=⒈得sinα=﹙﹣1+√5﹚/⒉(另一值不合题意)
∴cosα+cos(a)的六次方=﹙3√5-5)/⒉