已知sin2α=2/3则sin²(α-派/4)=?
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已知sin2α=2/3则sin²(α-派/4)=?
已知sin2α=2/3则sin²(α-派/4)=?
已知sin2α=2/3则sin²(α-派/4)=?
解
sin2a=2/3
由cos2a=1-2sin²a得:
sin²(a-π/4)
=[1-cos2(a-π/4)]/2
=[1-cos(2a-π/2)]/2
={1-cos[-(π/2-2a)]}/2
=[1-cos(π/2-2a)]/2
=(1-sin2a)/2
=(1-2/3)/2
=1/6
cos2α=cos²α-sin²α
=1-2sin²α
sin²α=(1-cos2α)/2
sin²(α-(π/4))
=[1-cos(2α-(π/2))]/2
=(1-sin2α)/2
解
sin2a=2/3
由cos2a=1-2sin²a得:
sin²(a-π/4)
=[1-cos2(a-π/4)]/2
=[1-cos(2a-π/2)]/2
={1-cos[-(π/2-2a)]}/2
=[1-cos(π/2-2a)]/2
=(1-sin2a)/2
=(1-2/3)/2
=1/6