es

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

4cos^2(x)=4-2sin^2(x)

Solución

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

Solución

x = 2 πn, x = π + 2 πn

+1

Grados

x = 0^{\circ} + 36 0^{\circ} n, x = 18 0^{\circ} + 36 0^{\circ} n

Pasos de solución

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

Restar

4 - 2 sin^{2} (x)

de ambos lados

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

Re-escribir usando identidades trigonométricas

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

Utilizar la identidad pitagórica:

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

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

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

Simplificar

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

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

Expandir

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

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

Poner los parentesis utilizando:

a (b - c) = ab - a c

a = 4, b = 1, c = sin^{2} (x)

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

Multiplicar los numeros:

4 \cdot 1 = 4

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

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

Simplificar

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

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

Agrupar términos semejantes

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

Sumar elementos similares:

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

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

- 4 + 4 = 0

= - 2 sin^{2} (x)

= - 2 sin^{2} (x)

= - 2 sin^{2} (x)

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

Dividir ambos lados entre

- 2

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

Dividir ambos lados entre

- 2

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

Dividir ambos lados entre

- 2

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

Simplificar

sin^{2} (x) = 0

sin^{2} (x) = 0

Aplicar la regla

x^{n} = 0 \Rightarrow x = 0

sin (x) = 0

Soluciones generales para

sin (x) = 0

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} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{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} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

x = 0 + 2 πn, x = π + 2 πn

x = 0 + 2 πn, x = π + 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, x = π + 2 πn

Ejemplos populares

sin(x)=sqrt(2)cos(x/2)

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

2sin(x)+1/(sin(x))=3

2 sin (x) + \frac{1}{sin ( x )} = 3

cos(x-pi/4)=(sqrt(3))/2

cos (x - \frac{π}{4}) = \frac{3}{2}

sec(θ)=3,sin(θ)<0

sec (θ) = 3, sin (θ) < 0

cos(x)tan(x)-cos(x)=0,0<= x<= 2pi

cos (x) tan (x) - cos (x) = 0, 0 \leq x \leq 2 π