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An equation is given. (Enter your answers as a comma-separated list. Let k be any integer.
Round terms to three decimal places where appropriate. If there is no solution, enter NO SOLUTION.)
1 − 2 sin(𝜃) = cos(2𝜃)
Find the solutions in the interval [0, 2𝜋).
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The solution in the post by @MathLover1 is INCORRECT.
I came to bring a correct solution.
Find the solutions in the interval [, ).
....use identity
...use identity
...factor
If then = 0 or = radians.
If then = .
ANSWER. In the given interval, there are three and only three solutions,
x = 0, x = = 1.571 radians and x = = 3.142 radians (rounded as requested).
Solved (correctly)
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The post is written INCORRECTLY.
If you need the solution in the interval [0,),
then you do not need to mention about "an arbitrary integer k".