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Popular >

cos^2(x)sec(x)=1

Solución

cos^{2} (x) sec (x) = 1

Solución

x = 2 πn

+1

Grados

x = 0^{\circ} + 36 0^{\circ} n

Pasos de solución

cos^{2} (x) sec (x) = 1

Restar

1

de ambos lados

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

Re-escribir usando identidades trigonométricas

- 1 + cos^{2} (x) sec (x)

Utilizar la identidad trigonométrica básica:

sec (x) = \frac{1}{cos ( x )}

= - 1 + cos^{2} (x) \frac{1}{cos ( x )}

cos^{2} (x) \frac{1}{cos ( x )} = cos (x)

cos^{2} (x) \frac{1}{cos ( x )}

Multiplicar fracciones:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot cos ^{2} ( x )}{cos ( x )}

Multiplicar:

1 \cdot cos^{2} (x) = cos^{2} (x)

= \frac{cos ^{2} ( x )}{cos ( x )}

Eliminar los terminos comunes:

cos (x)

= cos (x)

= - 1 + cos (x)

- 1 + cos (x) = 0

Mover

1

al lado derecho

- 1 + cos (x) = 0

Sumar

1

a ambos lados

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

Simplificar

cos (x) = 1

cos (x) = 1

Soluciones generales para

cos (x) = 1

cos (x)

tabla de valores periódicos con

2 πn

intervalos:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

x = 0 + 2 πn

x = 0 + 2 πn

Resolver

x = 0 + 2 πn : x = 2 πn

x = 0 + 2 πn

0 + 2 πn = 2 πn

x = 2 πn

x = 2 πn

Ejemplos populares

tan(x)=(9.3)/(7.5)

tan (x) = \frac{9.3}{7.5}

sin(α)+cos(α)=1

sin (α) + cos (α) = 1

2sin(θ)=sqrt(3)tan(θ)

2 sin (θ) = 3 tan (θ)

sin (x^{2} - 1) = 4

1-cos(x)=(2pi)/3

1 - cos (x) = \frac{2 π}{3}