SOLUTION: Solve the following algebraically for 0&#730; &#8804; x < 360&#730;: cos x = cos 2x Make sure you make a substitution for cos2x

Algebra ->  Trigonometry-basics -> SOLUTION: Solve the following algebraically for 0&#730; &#8804; x < 360&#730;: cos x = cos 2x Make sure you make a substitution for cos2x      Log On


   

Question 1117288: Solve the following algebraically for 0˚ ≤ x < 360˚: cos x = cos 2x
Make sure you make a substitution for cos2x
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
Given: cos%28x%29=cos%282x%29

Identity to use is cos%282x%29=-1%2B2cos%5E2%28x%29.

Given equation becomes cos%28x%29=2cos%5E2%28x%29-1,
2cos%5E2%28x%29-cos%28x%29-1=0.


letu=cos%28x%29.
2u%5E2-u-1=0
u=%281%2B-+sqrt%281%2B4%2A2%29%29%2F4
u=%281%2B-+3%29%2F4
system%28u=-1%2F2%2Cor%2C1%29
-
system%28cos%28x%29=-1%2F2%2C+or%2C+cos%28x%29=1%29
-
x can be any of 0, 120, 240 degree