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Answer 1 · 2016-12-29T17:38:02

The period is #=4pi#

The period of the sum of 2 periodic functions is the LCM of their periods.

The period of #sin(x/2)# is #=2/(1/2)pi=4pi#

The period of #cos(x/2)# is #=2/(1/2)pi=4pi#

#4=2*2#

LCM #(4,4)=4#

The LCM of #4pi# and #4pi# is #=4pi#

The period is #T=4pi#

graph{sin(x/2)-cos(x/2) [-12.76, 19.27, -7.66, 8.36]}