tan^2(x)=3-csc^2(x)

Solución

tan^{2} (x) = 3 - csc^{2} (x)

x = \frac{π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

Pasos de solución

tan^{2} (x) = 3 - csc^{2} (x)

Restar

3 - csc^{2} (x)

de ambos lados

tan^{2} (x) - 3 + csc^{2} (x) = 0

Re-escribir usando identidades trigonométricas

- 3 + csc^{2} (x) + \frac{1}{- 1 + csc ^{2} ( x )} = 0

Usando el método de sustitución

csc (x) = 2, csc (x) = - 2

csc (x) = 2 : x = \frac{π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn

csc (x) = - 2 : x = \frac{5 π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

Combinar toda las soluciones

x = \frac{π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

2 sin^{2} (u) = 1 + sin (u)

2 tan^{2} (θ) - 3 tan (θ) + 1 = 0

cos (x) = \frac{9}{17}

- 6 sin (c) + 0 = sin (c) - 3

tan (x) = \frac{11}{12}