Question #121ae

1 Answer
Nghi N
Jan 10, 2018

#0, 2pi#

Explanation:

#tan (x/2) = sin (x/2)#
#sin (x/2) = sin (x/2).cos (x/2)#
#sin (x /2) - sin (x/2).cos (x/2) = 0#
Put #sin (x/2)# into common factor:
#sin (x/2)(1 - cos (x /2)) = 0 #
Either factor should be zero.
a. #sin (x/2) = 0#
Unit circle --> #x/2 = 0# and #x/2 = pi# -->
x = 0 and #x = 2pi#
b. #cos (x/2) = 1#
Unit circle --> #x/2 = 0#, and #x/2 = 2pi# -->
x = 0 and #x = 4pi#
Answer for #(0, 2pi)#
#0, 2pi#

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