Question

Cot 2 2x – 4cot2x + 3 = 0

Answer 1

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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