SOLUTION: Write expressions that give all solutions to the following equation. (Express your answers in degrees. Let k be any integer. Enter your answers as a comma-separated list.) cos &#9

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Question 1016640: Write expressions that give all solutions to the following equation. (Express your answers in degrees. Let k be any integer. Enter your answers as a comma-separated list.)
cos θ/2 − cos θ = 1
Note: I have tried using the half-angle formal and squared boy sides to get rid of the square root. After that i found common denominators and did the algebraic stuff. I got 60, 180, and 300. I let k be an integer of 360k for each, but it was wrong. Thank you!

Answer by ikleyn(52909)   (Show Source): You can put this solution on YOUR website!
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Write expressions that give all solutions to the following equation. (Express your answers in degrees. Let k be any integer. Enter your answers as a comma-separated list.)
cos θ/2 − cos θ = 1
----------------------------------------------------------

 = .    (1)

For me, it is easier to introduce new variable  =  and to solve an equation for 

 -  = .   (2)

Surely, you know that  =  = . 

Substitute it into (2). You will get

 = ,   or

 = ,

 = .

Thus you have two separate equations 

1.   = 0  --->   =   --->   = , k = 0, +/-1, +/-2, . . . 

2.   =   --->   =   --->   = +/-  +    --->   = +/- + , k = 0, +/-1, +/-2, . . .


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