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）=?

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