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What are the exact solutions for the equation cos2x - cosx equals 0?
Wiki User
∙ 13y ago
2
Parker Braun
Wiki User
∙ 13y agoUse the trig identity
cos(2x) = 2 cos2(x) - 1
and substitute that equivalent quantity in the original equation.
2 cos2(x) - 1 - cos(x) = 0
To make things neater and easier to write, let "C" = "cos(x)" for a while.
2C2 - C - 1 = 0
(2C + 1) (C - 1) = 0
cos(x) = -1/2
x = 120° , 240° (and every angle that's 360° from one of these in either direction)
cos(x) = 1
x = 0° (and every positive and negative multiple of 360°)
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