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(52905)   (Show Source):
You can put this solution on YOUR website! .
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
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 =  . (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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