How do you find the value of ##tan45## using the half angle identity?

Using ##tan 90^o=+-oo##, tan 45^o=1

##tan 90^o=+-oo=(2 tan 45^o)/(1-tan^2 45^o##.

Equating the denominator to 0,

##tan^2 45^o=1 and tan 45^o=+-1##

The first quadrant tangent ##tan 45^o > 0##.

So, ##tan 45^o = 1##..

Note that tan x is discontinuous at x = ##90^## and that

limits ##tan 90+-^o=+-oo##.