sinx=根号5-1/2,求sin2(x-π/4)的值

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sinx=根号5-1/2,求sin2(x-π/4)的值
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sinx=根号5-1/2,求sin2(x-π/4)的值
sinx=根号5-1/2,求sin2(x-π/4)的值

sinx=根号5-1/2,求sin2(x-π/4)的值
sin2(x-π/4)
=sin(2x-π/2)
=-sin(π/2-2x)
=-cos2x
=-(1-2sin²x)
=2sin²x-1
=2[(√5-1)/2]²-1
=2*(6-2√5)/4-1
=2*2(3-√5)/4-1
=3-√5-1
=2-√5