Question

急，数学！！在线等

1，若tana~1/2，则tan(a π/4)的值为
2，在梯形abcd中，ad//bc，ad=2.bc=5点e.f分别在ab，cd上。且ef//ad，若ae/eb=3/4，则ef长为

Answer 1

1、tana=1/2
tan(a+π/4)=(tana+tanπ/4)/(1-tanatanπ/4)=(1+1/2)/(1-1/2)=3
同理tan(a-π/4)=1/3
2、连接ac交ef于k
ae/eb=3/4
ae/ab=ek/bc=3/7
bc=5，ek=15/7
同理kf=8/7
ef=ek+kf=15/7+8/7=23/7

Answer 2

tana=1/2 tan(a-π/4)=(tana-tanπ/4)/(1+tanatanπ/4)=-(1/2/3/2)=-1/3
tan(a+π/4)=(tana+tanπ/4)/(1-tanatanπ/4)=3
ad//bc,ef//ad,ae/ab=ef/bc ae/eb=3/4 eb/ae=4/3,ab/ae=7/3,ef=15/7