Show that [cosx+sinx]/[cosx-sinx]=1+[2tanx]/[1- tanx]

[cosx+sinx]/[cosx-sinx]=1+[2tanx]/[1- tanx]

= [1-tanx+2tanx]/[1-tanx]

= [1+tanx]/[1-tanx]

= [1+ sinx/cosx]/[1-sinx/cosx]

= [(cosx+sinx)/cosx]/[(cosx-sinx)/cosx]

= [cosx+sinx]/[cosx-sinx)]

Is it acceptable? Thank You.

from the left hand side,
1 + (2tan x/ 1- tanx)
= 1 + [ (2sin x/ cos x) / 1 - (sin x/ cos x) ]
= 1 + ( 2sin x/cos x)(cos x / cos x - sin x)
= 1 + [ 2sin x / (cos x - sin x)]
= (cos x - sin x + 2 sin x)/ (cos x -sin x)
= (cos x + 2sin x) / (cos x - sin x), proven.

Do women these days have Accountability problems? In marriages gone bad, why is it *always* the man's fault and never the "modern woman's"??