已知sinx=根号5-1/2,求sin2(x-π/4)的值根号5减去数字1.1没有根号

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已知sinx=根号5-1/2,求sin2(x-π/4)的值根号5减去数字1.1没有根号
已知sinx=根号5-1/2,求sin2(x-π/4)的值
根号5减去数字1.1没有根号

已知sinx=根号5-1/2,求sin2(x-π/4)的值根号5减去数字1.1没有根号
已知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
=-(1-2sin^2x) [sin^2x=(sinx)^2 ,^2表示平方〕
=2sin^2x-1
∴sin2(x-π/4)
=2[(√5-1)/2]^2-1
=2*(6-2√5)/4-1
=2*2(3-√5)/4-1
=3-√5-1
=2-√5

sin2(x-π/4)=sin(2x-π/2)
=-cos2x
=-(1-2sinx^2)
=2sinx^2-1
=1/2-√5/2