已知阿尔法是第三象限角,cos2阿尔法/3/5,则tan.(/4+2阿尔法)

Question

已知α是第二象限角,cos2α=-3/5,则tan(π/4+2α)=
我算来算去总是-1/7,答案是-7,为什么?

Answer 1

cos2a=2cos^2a-1
-3/5=2cos^2a-1
cos^2a=1/5,
a在第二象限,cosa<0,sina>0
cosa=-√5/5
sina=2√5/5
sin2a=2sinacosa=2*(2√5/5)*(-√5/5)=-4/5
tan2a=sin2a/cos2a=(-4/5)/(-3/5)=4/3
tan(π/4+2a)
=(tanπ/4+tan2a)/(1-tanπ/4*tan2a)
=(1+4/3)/(1-4/3)
=-7