How do you solve #5cos(2x)+1=3cos(2x)# and find all general solutions?

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How do you solve #5cos(2x)+1=3cos(2x)# and find all general solutions?

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Answer 1 · 2017-01-23T01:23:38

#pi/3 = kp#
#(5pi)/3 + kpi#

Explanation:

5cos 2x + 1 = 3cos 2x
2cos 2x = - 1
cos 2x = - 1/2
Trig table and unit circle give 2 solution arcs:
#2x = +- (2pi)/3 + 2kpi# --> #x = +- (2pi)/6 + kpi = +- pi/3 + kpi#
The arc #(5pi)/3# is co-terminal to the arc #(- pi)/3#.
General answers:
#x = pi/3 + kpi#
#x = (5pi)/3 + kpi#

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How do you solve #5cos(2x)+1=3cos(2x)# and find all general solutions?

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