William W. answered • 11/16/20
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2cos(x) + √2 = 0
2cos(x) = -√2
cos(x) = -√2/2
Using the unit circle we can see that cos(x) = -√2/2 when x = 3π/4 and 5π/4
Since there are no domain restrictions, we must make the answer generic to any number of times around the circle. So, assuming k is any integer, then x = 3π/4 + 2πk and x = 5π/4 + 2πk
