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

Solución

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

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

cos^{2} (x) - cos (x) = 2

sin (x) = 0.67

sin (x) = 0.69

4 cos^{2} (x) - 4 = 15 cos (x)

(cos (θ) - 1) sin (θ) = 0