Find all solutions for the following equations sin(2x)+sin(π/2-x)=0 ?

1 Answer
Nghi N
May 14, 2018

#pi/2; (3pi)/2 ; (7pi)/6; (11pi)/6# #(+ 2kpi)#

Explanation:

#sin 2x + sin (pi/2 - x) = 0#
Note. sin 2x = 2sin x.cos x
#sin (pi/2 - x) = cos x#
Therefor,
#2sin x.cos x + cos x = 0#
#cos x(2sin x + 1) = 0#
Either factor should be zero -->
a. #cos x = 0#
Unit circle gives -->
#x = pi/2 + 2kpi#, and
#x = (3pi)/2 + 2kpi#
b. #2sin x + 1 = 0# --> #sin x = - 1/2#
Unit circle gives -->
#x = (7pi)/6 + 2kpi#, and
#x = (11pi)/6 + 2kpi#

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