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Popular >

csc(x)=1+cot(x)

Solución

csc (x) = 1 + cot (x)

x = \frac{π}{2} + 2 πn

Pasos de solución

csc (x) = 1 + cot (x)

Restar

1 + cot (x)

de ambos lados

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

Expresar con seno, coseno

\frac{1}{sin ( x )} - 1 - \frac{cos ( x )}{sin ( x )} = 0

Simplificar

\frac{1}{sin ( x )} - 1 - \frac{cos ( x )}{sin ( x )} : \frac{1 - cos ( x ) - sin ( x )}{sin ( x )}

\frac{1 - cos ( x ) - sin ( x )}{sin ( x )} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

1 - cos (x) - sin (x) = 0

Sumar

sin (x)

a ambos lados

1 - cos (x) = sin (x)

Elevar al cuadrado ambos lados

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

Restar

sin^{2} (x)

de ambos lados

(1 - cos (x))^{2} - sin^{2} (x) = 0

Re-escribir usando identidades trigonométricas

- 2 cos (x) + 2 cos^{2} (x) = 0

Usando el método de sustitución

cos (x) = 1, cos (x) = 0

cos (x) = 1 : x = 2 πn

cos (x) = 0 : x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

Combinar toda las soluciones

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

Verificar las soluciones sustituyendo en la ecuación original

x = 2 πn, x = \frac{π}{2} + 2 πn

Siendo que la ecuación esta indefinida para:

2 πn

x = \frac{π}{2} + 2 πn

6 sin^{2} (x) = 5 sin (x)

cos (π x) = 1

\frac{( 3 )}{( cos ( x ) )} = 8 - 5 tan (x)

x, π + 3 arccos (x + 1) = 0

cos (x + 4 0^{\circ}) = 0.3