Answer: Choice A) 45 + k*90
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Work Shown:
2*tan(x) = 2*cot(x)
2*tan(x) = 2*(1/tan(x))
2*y = 2*(1/y) .... let y = tan(x)
2y = 2/y
2y^2 = 2
2y^2 - 2 = 0
2(y^2 - 1) = 0
y^2 - 1 = 0
(y+1)(y-1) = 0
y+1 = 0 or y-1 = 0
y = -1 or y = 1
tan(x) = -1 or tan(x) = 1
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If tan(x) = -1 then x = 135 or x = 315
If tan(x) = 1, then x = 45 or x = 225
This is for
In more general terms,
x = 45 + k*90
where k is an integer.