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

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Answer 1 · 2016-07-20T14:35:36

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#.