f(t)=梗号(1-t)/(1+t),g(x)=cosx*f(sinx)+sinx*f(cosx),化简到Asin(wx
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f(t)=梗号(1-t)/(1+t),g(x)=cosx*f(sinx)+sinx*f(cosx),化简到Asin(wx+¤)+b的形式
g(x)=cosx*f(sinx)+sinx*f(cosx),
=cosx*√[(1-sinx)/(1+sinx)]+sinx*√[(1-cosx)/(1+cosx)]
=cosx*√[(1-sinx)^2/(1+sinx)(1-sinx)]+sinx*√[(1-cosx)^2/(1+cosx)(1-cosx)]
=cosx*√[(1-sinx)^2/(cosx)^2]+sinx*√[(1-cosx)^2/(sinx)^2]
=1-sinx+1-cosx
=2-(sinx+cosx)
=-(sinx+cosx)+2
=-√2(√2/2sinx+√2/2cosx)+2
=-√2(sinxcosπ/4+cosxsinxπ/4)+2
=-√2sin(x+π/4)+2
=cosx*√[(1-sinx)/(1+sinx)]+sinx*√[(1-cosx)/(1+cosx)]
=cosx*√[(1-sinx)^2/(1+sinx)(1-sinx)]+sinx*√[(1-cosx)^2/(1+cosx)(1-cosx)]
=cosx*√[(1-sinx)^2/(cosx)^2]+sinx*√[(1-cosx)^2/(sinx)^2]
=1-sinx+1-cosx
=2-(sinx+cosx)
=-(sinx+cosx)+2
=-√2(√2/2sinx+√2/2cosx)+2
=-√2(sinxcosπ/4+cosxsinxπ/4)+2
=-√2sin(x+π/4)+2
f(t)=梗号(1-t)/(1+t),g(x)=cosx*f(sinx)+sinx*f(cosx),化简到Asin(wx
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