8 + 4 cos(2x) = 12 cos(x)?
Find all values of x in the interval [0, 2π]
I tried to solve and go cos=1, which means x= π/2? but that isn't correct. :( please help.
Find all values of x in the interval [0, 2π]
I tried to solve and go cos=1, which means x= π/2? but that isn't correct. :( please help.
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Verified answer
8 + 4 cos(2x) = 12 cos(x)
8 + 4 [2cos²(x) − 1] = 12 cos(x)
8cos²(x) − 12cos(x) + 4 = 0
2cos²(x) − 3cos(x) + 1 = 0
[2cos(x) − 1][cos(x) − 1] = 0
cos(x) = ½ or 1
x = 5π/3, π/3, 0, 2π.
x=0