求证:1+sin2x/cos2x=tan(π/4+x)

sin^4(Π/16)+sin^4( 3Π /16)+sin^4( 5Π/16)+sin^4(7Π/16)
=sin^4(Π/16)+sin^4(7Π/16)+sin^4( 3Π /16)+sin^4( 5Π/16)
=sin^4(Π/16)+cos^4(Π/16)+sin^4( 3Π /16)+cos^4( 3Π/16)
=1-2sin^2(Π/16)cos^2(Π/16)+1-2sin^2(3Π/16)cos^2(3Π/16)
=2-(sinΠ/4)^2/2-(sin3Π/4)^2/2
=2-1/2
=3/2