x = 9.21° or x = 22.5°
cot²2x – 4cot2x + 3 = 0
Let cot2x = y
y² - 4y + 3 = 0
Factorizing, we have
y² - y - 3y + 3 = 0
y(y - 1) -3(y - 1) = 0
(y - 1)(y - 3) = 0
y - 1 = 0 or y - 3 = 0
y = 1 or y = 3
Since cot2x = y
cot2x = 1 or cot2x = 3
1/tan2x = 1 or 1/tan2x = 3
tan2x = 1 or tan2x = 1/3
2x = tan⁻¹(1) or 2x = tan⁻¹(1/3)
2x = 45° or 2x = 18.43°
x = 45°/2 or x = 18.43°/2
x = 22.5° or x = 9.21°
So, x = 9.21° or x = 22.5°
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