Remember the basic trig identity
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We can move the cosine term to the right side to get
We can then replace
in the original equation and basically factor the resulting equation like a quadratic:
Then, we can see that
either equals
or
. But since the range of cosine is only from
, cosine can't equal
at all! So, you just have to solve for x when
, which is when
(The last part of the solution says that k can be any integer.)
If you only want solutions in the range
, then your answer is just