tan2α+1/tan2α=2 则sinαcosα=

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tan2α+1/tan2α=2 则sinαcosα=

tan2α+1/tan2α=2 则sinαcosα=
tan2α+1/tan2α=2 则sinαcosα=

tan2α+1/tan2α=2 则sinαcosα=
tan2α+1/tan2α=2
sin(2α)/cos(2α)+cos(2α)/sin(2α)=2
1/[sin(2α)cos(2α)]=2
sin(4α)=1
4α=2kπ+π/2
2α=kπ+π/4
sinαcosα=sin(2α)/2=sin(kπ+π/4)/2=±√2/4

tan²2α-2tan2α+1=0
tan2α=1
sin2α=± 根号2/2
sinαcosα= 1/2 sin2α = ± 根号2/4

tan2α+1/tan2α=sin2a/cos2a+cos2a/sin2a=1/sin2acos2a=2
sin2acos2a=1 /2
设x=sin2a
│x│√(1-x^2)=1/2
x^2(1-x^2)=1/4
x^2=1/2
x=±√2/2
sinacosa=1/2sin2a=x/2=±√2/4