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Popular >

sec(x)+sin^2(x)+cos^2(x)=tan^2(x)

Solución

sec (x) + sin^{2} (x) + cos^{2} (x) = tan^{2} (x)

Solución

x = π + 2 πn, x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

+1

Pasos de solución

sec (x) + sin^{2} (x) + cos^{2} (x) = tan^{2} (x)

Restar

tan^{2} (x)

de ambos lados

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

Expresar con seno, coseno

\frac{cos ( x ) + cos ^{4} ( x ) - sin ^{2} ( x ) + cos ^{2} ( x ) sin ^{2} ( x )}{cos ^{2} ( x )} = 0

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

cos (x) + cos^{4} (x) - sin^{2} (x) + cos^{2} (x) sin^{2} (x) = 0

Factorizar

cos (x) + cos^{4} (x) - sin^{2} (x) + cos^{2} (x) sin^{2} (x) : (1 + cos (x)) (cos (x) (cos^{2} (x) + 1 - cos (x)) + sin^{2} (x) (- 1 + cos (x)))

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

Resolver cada parte por separado

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

1 + cos (x) = 0 : x = π + 2 πn

cos (x) (cos^{2} (x) + 1 - cos (x)) + sin^{2} (x) (- 1 + cos (x)) = 0 : x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Combinar toda las soluciones

x = π + 2 πn, x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Ejemplos populares

4sin^2(x)-3=4,sin(2x)-3=0

4 sin^{2} (x) - 3 = 4, sin (2 x) - 3 = 0

tan^2(θ)+tan(θ)=6,0<= θ<180

tan^{2} (θ) + tan (θ) = 6, 0 \leq θ < 18 0^{\circ}

sin(2x)=5sin(x)

sin (2 x) = 5 sin (x)

2cos^2(θ)-4cos(θ)-1=-5cos(θ)

2 cos^{2} (θ) - 4 cos (θ) - 1 = - 5 cos (θ)

-2sin^2(x)-sin(x)+3=0

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