已知tan(π/4-a)=-1/2,求cos2a的值等于

已知tan(π/4-a)=-1/2,求cos2a的值等于
已知tan(π/4-a)=-1/2,求cos2a的值等于

已知tan(π/4-a)=-1/2,求cos2a的值等于
tana
=tan[π/4-(π/4-a)]
=[tan(π/4)-tan(π/4-a)]/[1+tan(π/4)tan(π/4-a]
=(1+1/2)/(1-1/2)
=3
∴ cos2a
=cos²a-sin²a
=(cos²a-sin²a)/(cos²a+sin²a)
同除以cos²a
=(1-tan²a)/(1+tan²a)
=(1-9)/(1+9)
=-4/5

tan(π/4-a)=-1/2
(1-tana)/(1+tana)=-1/2
2-2tana=-1-tana
tana=3
sina/cosa=3
sina=3cosa
sin²a+cos²a=1
10cos²a=1
cos²a=1/10
cos2a=2cos²a-1
=1/5-1
=-4/5

啊啊啊

tan(a-π/4)=-tan(π/4-a)=-2
tana=tan(a-π/4+π/4)
=(tan(a-π/4)+tan(π/4))/(1-tan(a-π/4)tan(π/4))
=-1/3
cos2a=(1-(tana)^2)/(1+(tana)^2)
=4/5