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2tan(x)+cos(x)=0

Solución

2 tan (x) + cos (x) = 0

x = - 0.42707 \dots + 2 πn, x = π + 0.42707 \dots + 2 πn

Pasos de solución

2 tan (x) + cos (x) = 0

Expresar con seno, coseno

2 \cdot \frac{sin ( x )}{cos ( x )} + cos (x) = 0

Simplificar

2 \cdot \frac{sin ( x )}{cos ( x )} + cos (x) : \frac{2 sin ( x ) + cos ^{2} ( x )}{cos ( x )}

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

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

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

Restar

cos^{2} (x)

de ambos lados

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

Elevar al cuadrado ambos lados

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

Restar

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

de ambos lados

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

Factorizar

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

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

Resolver cada parte por separado

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

2 sin (x) + cos^{2} (x) = 0 : x = arcsin (1 - 2) + 2 πn, x = π + arcsin (- 1 + 2) + 2 πn

2 sin (x) - cos^{2} (x) = 0 : x = arcsin (- 1 + 2) + 2 πn, x = π - arcsin (- 1 + 2) + 2 πn

Combinar toda las soluciones

x = arcsin (1 - 2) + 2 πn, x = π + arcsin (- 1 + 2) + 2 πn, x = arcsin (- 1 + 2) + 2 πn, x = π - arcsin (- 1 + 2) + 2 πn

Verificar las soluciones sustituyendo en la ecuación original

x = arcsin (1 - 2) + 2 πn, x = π + arcsin (- 1 + 2) + 2 πn

Mostrar soluciones en forma decimal

x = - 0.42707 \dots + 2 πn, x = π + 0.42707 \dots + 2 πn

cos (2 x) + sec (2 x) = 11

cos^{2} (t) = \frac{3}{4}

5 tan (x) - 4 = 0

4 sin (x) = - cos^{2} (x) + 1, 0 \leq x \leq 2 π

3 tan (x) sin (x) - 2 tan (x) = 0