How do you prove cosx/2+sinx/2= 1+tanx/2 ?

1 Answer
Nghi N.
Jun 28, 2018

Impossible identity

Explanation:

#cos (x/2) + sin (x/2) = sqrt2cos (x/2 - pi/4)#.
It can't be equal to #(1 + tan (x/2)#. This identity is impossible.
Example:
x = 60^@ --> #sin (x/2) = sin 30 = 1/2#--> #cos x = cos 30 = sqrt3/2#
--> #tan (x/2) = tan 30 = sqrt3/3#.
#cos (x/2) + sin (x/2) = 1/2 + sqrt3/2 != 1 + sqrt3/3 = 1 + tan (x/2)#
Therefor, the identity is impossible.

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