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Answer 1
Donald Carr
To find the maximum number of solutions to the equation sin(2x) + cos(x) = 1 on the interval [0, 2π], we first rewrite sin(2x) as 2sin(x)cos(x). Thus, the equation becomes 2sin(x)cos(x) + cos(x) = 1. Factoring out cos(x), we get cos(x)(2sin(x) + 1) = 1. Solving cos(x) = 0 and 2sin(x) + 1 = 1, we find that there are a maximum of 4 solutions in the given interval.
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