Find all values of x in the interval [0, 2pi] that satisfy the equation: 2+cos 2x=3cos x

Rapsinincke 2022-07-16 Answered
Find all values of x in the interval [ 0 , 2 π ] that satisfy the equation:
2 + cos 2 x = 3 cos x
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Answers (2)

Ronald Hickman
Answered 2022-07-17 Author has 18 answers
2 + cos 2 x = 3 cos x
cos 2 x = 2 cos 2 x 1
= 1 2 sin 2 x
2 + 2 cos 2 x 1 = 3 cos x
2 cos 2 x 1 = 3 cos x
2 cos 2 x 3 cos x + 1 = 0
( 2 cos x 1 ) ( cos x 1 ) = 0
cos x = 1 2       cos x = 1
x = π 3 ; 5 π 3       x = 0 ; 2 π
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Jeffrey Jordon
Answered 2022-08-01 Author has 2313 answers

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