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In this problem, we need to get the angles to be the same.
So we're going to take that cosine 2X and do a substitution
and one of the formulas for cosine 2X is 1 -, 2 sine squared
X.
Then we're going to have that plus sine X equaling one.
I chose that formula because I wanted the trig functions to be
in the same, so I wanted sine and sine.
If we now take everything to one side because I want to get rid
of the one the ones would cancel, we get negative sine -2
sine squared X plus sine X equaling 0.
From there I could factor out a negative sine X and now we have
two things that multiply to give us zero.
So we're going to set each one equal to 0, sine X = 0 and two
sine X - 1 = 0.
So now you need to think about it.
What values on your unit circle as sine X0 and at what values on
your unit circle is sine X1 half?
Remember it's asking for only the values in between 0 and 2π.