Question

Tang x + 3. cotan x = 4

Answer 1

Respuesta:

x₁ = 45º

x₁ = π / 4

x₂ = 71,56º

Explicación:

tan(x) + 3cot(x) = 4

1 / cot(x) + 3cot(x) = 4

(1 + 3cot²(x)) / cot(x) = 4

1 + 3cot²(x) = 4cot(x)

1 + 3cot²(x) - 4cot(x) = 0

3cot²(x) - 4cot(x) + 1 = 0             multiplicados 3 y sumados -4

(3cot(x) - 3)(3cot(x) - 1) / 3 = 0

3(cot(x) - 1)(3cot(x) - 1) / 3 = 0

(cot(x) - 1)(3cot(x) - 1) = 0

cot(x) - 1 = 0

cot(x) = 1

x₁ = arccot(1)

x₁ = 45º

x₁ = π / 4

3cot(x) - 1 = 0

3cot(x) = 1

cot(x) = 1 / 3

x₂ = arccot(1 / 3)

x₂ = 71,56º