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Popular >

sec(x)-sec(x)tan(x)=0

Solución

sec (x) - sec (x) tan (x) = 0

Solución

x = \frac{π}{4} + πn

+1

Grados

x = 4 5^{\circ} + 18 0^{\circ} n

Pasos de solución

sec (x) - sec (x) tan (x) = 0

Factorizar

sec (x) - sec (x) tan (x) : - sec (x) (tan (x) - 1)

sec (x) - sec (x) tan (x)

Factorizar el termino común

- sec (x)

= - sec (x) (- 1 + tan (x))

- sec (x) (tan (x) - 1) = 0

Resolver cada parte por separado

sec (x) = 0 or tan (x) - 1 = 0

sec (x) = 0 :

Sin solución

sec (x) = 0

sec (x) \leq - 1 or sec (x) \geq 1

Sin soluci \overset{o}{ˊ} n

tan (x) - 1 = 0 : x = \frac{π}{4} + πn

tan (x) - 1 = 0

Mover

1

al lado derecho

tan (x) - 1 = 0

Sumar

1

a ambos lados

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

Simplificar

tan (x) = 1

tan (x) = 1

Soluciones generales para

tan (x) = 1

tan (x)

tabla de valores periódicos con

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} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

x = \frac{π}{4} + πn

x = \frac{π}{4} + πn

Combinar toda las soluciones

x = \frac{π}{4} + πn

Ejemplos populares

4sin^2(x)=3,0<= x<= 180

4 sin^{2} (x) = 3, 0 \leq x \leq 18 0^{\circ}

sin(x+30)=2cos(x)

sin (x + 3 0^{\circ}) = 2 cos (x)

(3cos(x)+2sin(x))^2+5sin^2(x)=9-3sqrt(3)

(3 cos (x) + 2 sin (x))^{2} + 5 sin^{2} (x) = 9 - 33

7cos(2x)=7sin^2(x)+5

7 cos (2 x) = 7 sin^{2} (x) + 5

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

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