2sec^2(x)+tan^2(x)-3=0

Solución

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

x = \frac{π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn, x = \frac{7 π}{6} + 2 πn

Pasos de solución

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

Re-escribir usando identidades trigonométricas

- 4 + 3 sec^{2} (x) = 0

Usando el método de sustitución

sec (x) = \frac{2 3}{3}, sec (x) = - \frac{2 3}{3}

sec (x) = \frac{2 3}{3} : x = \frac{π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

sec (x) = - \frac{2 3}{3} : x = \frac{5 π}{6} + 2 πn, x = \frac{7 π}{6} + 2 πn

Combinar toda las soluciones

x = \frac{π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn, x = \frac{7 π}{6} + 2 πn

tan (x) = \frac{1}{2}

csc (x) + cot (x) = 1

2 sin (x) + csc (x) = 0

2 sin (x) = 3

sin (x) + 1 = 0