SOLUTION: Solve the following algebraically for 0˚ ≤ x < 360˚: cos x = cos 2x

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Question 1138003: Solve the following algebraically for 0˚ ≤ x < 360˚: cos x = cos 2x
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
given:cos+%28x%29+=+cos+%282x%29 , 0%3C=x%3C=360°
cos+%28x%29+-cos+%282x%29+=0..........use the following identity :+cos++%282x+%29=+-1%2B2+cos%5E2+%28x%29
cos+%28x%29+-%28-1%2B2+cos%5E2+%28x%29%29+=0
cos+%28x%29+%2B1-2cos%5E2+%28x%29+=0...let cos%28x%29=u
u+%2B1-2u%5E2+=0
-2u%5E2%2Bu+%2B1+=0
-2u%5E2%2B2u-u++%2B1+=0
-%282u%5E2-2u%29-%28u+-1%29+=0
-%282u+%2B+1%29+%28u+-+1%29=0
solutions:
-%282u+%2B+1%29+=0=>-2u-1=0=>-1=2u=>u=-1%2F2
%28u+-+1%29=0=>u=1

so, since cos%28x%29=u we have:

cos+%28x%29+=-1%2F2 or
cos+%28x%29+=1
if cos%28x%29=-1%2F2, and 0=x%3C=360°, then
x=120°,+x=240°
if cos%28x%29=1, and 0=x%3C=360°, then

x=0, x=360°

combine all solutions:x=0, x=120°,+x=240°, x=360°