Question 903574: Find all values of x in the interval [0, 2π] that satisfy the equation.
10 + 5 cos(2x) = 15 cos(x)
x =
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Find all values of x in the interval [0, 2π] that satisfy the equation.
10 + 5 cos(2x) = 15 cos(x)
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10 + 5 (2cos^2(x)-1) = 15 cos(x)
10 + 10cos^2(x)-5=15 cos(x)
10cos^2(x)-15cos(x)+5=0
2cos^2(x)-3cos(x)+1=0
(2cos(x)-1)(cosx-1)=0
cos(x)=1/2
x=π/3, 5π/3
or
cosx=1
x=0
x=π/3, 5π/3 ,0
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