化简sin4a/[4sin*2(π/4-a)tan(π/4-a)]

化简sin4a/[4sin*2(π/4-a)tan(π/4-a)]
化简sin4a/[4sin*2(π/4-a)tan(π/4-a)]

化简sin4a/[4sin*2(π/4-a)tan(π/4-a)]
sin4a/[4sin*2(π/4-a)tan(π/4-a)]
=sin4a/[8sin(π/4-a)cos(π/4-a)tan(π/4-a)]
=sin4a/[4sin(π/4-a)sin(π/4-a)]
=sin4a/[2-2cos(π/2-2a)]
=sin4a/[2-2sin2a]

化简sin4α/[4sin*2(π/4-α)tan(π/4-α)]
原式=sin4α/[8sin(π/4-α)cos(π/4-α)tan(π/4-α)]=sin4α/8sin²(π/4-α)=sin4α/{4[1-cos2(π/4-α)]}
=sin4α/{4[1-cos(π/2-2α)]=sin4α/[4(1-sin2α)]=2sin2αcos2α/[4(1-2sinα...

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化简sin4α/[4sin*2(π/4-α)tan(π/4-α)]
原式=sin4α/[8sin(π/4-α)cos(π/4-α)tan(π/4-α)]=sin4α/8sin²(π/4-α)=sin4α/{4[1-cos2(π/4-α)]}
=sin4α/{4[1-cos(π/2-2α)]=sin4α/[4(1-sin2α)]=2sin2αcos2α/[4(1-2sinαcosα)]
=sin2α(cos²α-sin²α)/[2(cosα-sinα)²]=sin2α(cosα+sinα)/[2(cosα-sinα)]
=(1/2)sin2α[(1+tanα)/(1-tanα)]=sinαcosαtan(π/4+α)

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