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

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Question 1180337: 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!

Solve the following algebraically for 0˚ ≤ x < 360˚:

cos+%28x+%29=+cos+%282x%29
cos+%28x+%29=+cos%5E2%28x%29+-+sin%5E2%28x%29
cos%5E2%28x%29+-cos+%28x+%29-+sin%5E2%28x%29=0..............use sin%5E2%28x%29=1-cos%5E2%28x%29+
cos%5E2%28x%29+-cos+%28x+%29-+%281-cos%5E2%28x%29+%29=0
cos%5E2%28x%29+-cos+%28x+%29-+1%2Bcos%5E2%28x%29+=0
2cos%5E2%28x%29+-cos+%28x+%29-+1+=0+.............factor
%28cos+%28x+%29+-+1%29+%282cos+%28x+%29+%2B+1%29+=+0
solutions:
cos+%28x+%29+=1->cos%5E-1+%281+%29->cos%5E-1+%281+%29=highlight%280%29°
cos+%28x+%29+=-1%2F2->cos%5E-1+%28-1%2F2+%29=%28%282pi%29%2F3%29%2An
n=1
%28%282pi%29%2F3%29%2A1=++highlight%28120%29°
n=1
%28%282pi%29%2F3%29%2A2=%284pi%29%2F3+=highlight%28240%29°