tan(a+π⼀4)=3⼀4则tan2a=

tan(a+π/4)=(tana+tan45)/(1-tana tan45)
=(tana+1)/(1-tana)
=3/4
所以4tana+4=3-3tana
所以tana=-1/7
所以tan2a=2tana/(1-tan^2 a)
=(-2/7)/(1-1/49)
=(-2/7)/(48/49)
= -7/24

tan(a+π/4)=(tana+1)/(1-tana)=3/4, 4tana+4=3-3tana tana=-1/7
tan2a=2tana/(1-tan^2a)=-2/[7(1-1/49)]=-7/24

tan(2a+π/2)=
2(tan(a+π/4))/(1-tan(a+π/4)tan(a+π/4))=2*3/4/(1-9/16)=24/7
tan(2a+π/2)=(sin2acosπ/2+sinπ/2cos2a)/(cos2acosπ/2-sin2asinπ/2)=-1/tan2a
tan2a=-7/24