Question

α为锐角，且tan(π/4+α)=2，求(sin2αcosα-sinα)/cos2α

Answer 1

tan(π/4+α)=(1+tana)/(1-tana)=2
tana=1/3
cosa=3sina
sin^2a+cos^2a=1 a为锐角
sina=√10/10 cosa=3√10/10
sin2a=2sinacosa=3/5 cos2a=cos^2a-sin^2a=4/5
(sin2αcosα-sinα)/cos2α
=(3/5*3√10/10-√10/10)/(4/5)
=(4√10/50)/(4/5)
=√10/10

Answer 2

上面的太麻烦了。先应化简！！！
(sin2αcosα-sinα)/cos2α
=(2sinacosacosa-sina)/cos2a
=(2cos^2a-1)sina/(cos2a)
=cos2asina/cos2a=sina
tan(π/4+α)=tanπ/4+tana)/(1-tanπ/4tana)=（1+tana)/(1-tana)=2
tana=1/3
tan^2a=1/9
sin^2a/cos^2a=1/9
sina^2a=1/9(1-sin^2a)
sina=根号10/10
原式=sina=根号10/10