Answer:
cosx(1-sinx) and ±√(1-cosx)/(1+cosx
Step-by-step explanation:
Given
let x/2 =a then
1-cosx/sinx will be
1-cos2a/sin2a
using cos2x=1-2sin^2x
using sin2x= 2cosxsinx
1-1+2sin^2a/2cosasina
2sina/2cosa
sina/cosa
tana
a=x/2
tana=tanx/2
if x/2=a thensinx/(1+cosx) will be
sin2a/1+cos2a
using sin2x=2cosxsinx and cos2x=-1+2cos^2x
2cosasina/1-1+2cos^2a
2sina/2cosa
sina/cosa
tana
as a=x/2
tana=tanx/2
1-cosx/sinx , sinx/(1+cosx) are identities of tan(x/2)
Both cosx(1-sinx) and ±√(1-cosx)/(1+cosx) are not identities of tan(x/2)!
