已知sin(π/4+α)+sin(π/4-α)=根号2/3,(1)求sinα(2)求sin(α-π/4)/1-sin2α
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已知sin(π/4+α)+sin(π/4-α)=根号2/3,(1)求sinα(2)求sin(α-π/4)/1-sin2α-cos2α
sin(π/4+α)+sin(π/4-α)
=sinπ/4cosα+cosπ/4sinα+sinπ/4cosα-cosπ/4sinα
=2sinπ/4cosα
=2*√2/2cosα
=√2cosα
√2cosα=√2/3
cosα=1/3
sinα=±2√2/3
sin(α-π/4)/(1-sin2α-cos2α )
=sin(α-π/4)/[1-sin2α-2(cosα)^2+1]
=sin(α-π/4)/[2-2(cosα)^2-sin2α]
=sin(α-π/4)/[2(sinα)^2-2sinαcosα]
=sin(α-π/4)/[2sinα(sinα-cosα)]
=sin(α-π/4)/[2√2sinα(√2/2sinα-√2/2cosα)]
=sin(α-π/4)/[2√2sinαsin(α-π/4)]
=1/(2√2sinα)
=1/[2√2*(±2√2/3)]
=1/(±8/3)
=±3/8
=sinπ/4cosα+cosπ/4sinα+sinπ/4cosα-cosπ/4sinα
=2sinπ/4cosα
=2*√2/2cosα
=√2cosα
√2cosα=√2/3
cosα=1/3
sinα=±2√2/3
sin(α-π/4)/(1-sin2α-cos2α )
=sin(α-π/4)/[1-sin2α-2(cosα)^2+1]
=sin(α-π/4)/[2-2(cosα)^2-sin2α]
=sin(α-π/4)/[2(sinα)^2-2sinαcosα]
=sin(α-π/4)/[2sinα(sinα-cosα)]
=sin(α-π/4)/[2√2sinα(√2/2sinα-√2/2cosα)]
=sin(α-π/4)/[2√2sinαsin(α-π/4)]
=1/(2√2sinα)
=1/[2√2*(±2√2/3)]
=1/(±8/3)
=±3/8
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