sinx+cosx=根号2,那吗sin∧4x+cos∧4x的值为
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sinx+cosx=根号2,那吗sin∧4x+cos∧4x的值为
![sinx+cosx=根号2,那吗sin∧4x+cos∧4x的值为](/uploads/image/z/14492712-48-2.jpg?t=sinx%2Bcosx%3D%E6%A0%B9%E5%8F%B72%2C%E9%82%A3%E5%90%97sin%E2%88%A74x%2Bcos%E2%88%A74x%E7%9A%84%E5%80%BC%E4%B8%BA)
(sinx+cosx)^2 = 2
2sinxcosx =1
sin2x=1
(sinx+cosx)^4 = 4
(sinx)^4+4(sinx)^3cosx+6(sinxcosx)^2 + 4sinx(cosx)^3 + (cosx)^4=4
[(sinx)^4+(cosx)^4]+4sinxcosx + 6(sinxcosx)^2 =4
(sinx)^4+(cosx)^4 = 4- 2sin2x- (3/2)(sin2x)^2
=4- 2- 3/2
= 1/2
2sinxcosx =1
sin2x=1
(sinx+cosx)^4 = 4
(sinx)^4+4(sinx)^3cosx+6(sinxcosx)^2 + 4sinx(cosx)^3 + (cosx)^4=4
[(sinx)^4+(cosx)^4]+4sinxcosx + 6(sinxcosx)^2 =4
(sinx)^4+(cosx)^4 = 4- 2sin2x- (3/2)(sin2x)^2
=4- 2- 3/2
= 1/2
sinx+cosx=根号2,那吗sin∧4x+cos∧4x的值为
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