已知2tanx/(1+tan^2x)=3/5,求sin^2(π/4+x)的值
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已知2tanx/(1+tan^2x)=3/5,求sin^2(π/4+x)的值
sin2x
=2sinx*cosx
=2sinx/cosx*cos^2 x
=2tanx/(1/cos^2x)
=2tanx/[(sin^2x+cos^2x)/cos^2x]
=2tanx/(1+tan^2x)
2tanx/(1+tan^2x) =3/5
sin2x=3/5
Cos2A=CosA^2-SinA^2=1-2SinA^2
sin^2(π/4 +x)
=[1-cos2(π/4 +x)]/2
=[1-cos(π/2 +2x)]/2
=[1+3/5]/2
=4/5
=2sinx*cosx
=2sinx/cosx*cos^2 x
=2tanx/(1/cos^2x)
=2tanx/[(sin^2x+cos^2x)/cos^2x]
=2tanx/(1+tan^2x)
2tanx/(1+tan^2x) =3/5
sin2x=3/5
Cos2A=CosA^2-SinA^2=1-2SinA^2
sin^2(π/4 +x)
=[1-cos2(π/4 +x)]/2
=[1-cos(π/2 +2x)]/2
=[1+3/5]/2
=4/5
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