if tan(x/2)=senx and cosx is not zero, find tanx

Question

a) -1 b) -(3^1/2)/3 c) 1/2 d) 1 e) 0

Answer 1

d) 1

Answer 2

Please clarify your typo
is it
tan(x/2)=sinx
or
tan(x/2)=secx

btw, the bot's answer of tanx = 1, would give us 45°
then tan(22.5) = sin45 would be false, and
then tan(22.5) = sec 45 would also be false
so the robot tutor would be wrong in either case.

but tan(22.5) = .414213562..
sec(45) = 1.414213562... , interesting.

Answer 3

since tan(x/2) = sinx/(1+cosx), we have
sinx/(1+cosx) = sinx
so sinx=0 gives x=0
and tanx = 0

or
1/(1+cosx) = 1
1 = 1+cosx
but cosx≠0 so that's out