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cos(2x)=cos^2(x)

Solución

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

x = 2 πn, x = π + 2 πn

Grados

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

Pasos de solución

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

Restar

cos^{2} (x)

de ambos lados

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

Re-escribir usando identidades trigonométricas

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

Utilizar la identidad trigonométrica del ángulo doble:

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

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

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

Simplificar

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

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

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

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

Poner los parentesis

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

Aplicar las reglas de los signos

+ (- a) = - a

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

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

Sumar elementos similares:

cos (2 x) - cos (2 x) = 0

= - sin^{2} (x)

= - sin^{2} (x)

- sin^{2} (x) = 0

Dividir ambos lados entre

- 1

- sin^{2} (x) = 0

Dividir ambos lados entre

- 1

- sin^{2} (x) = 0

Dividir ambos lados entre

- 1

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

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

tan (\frac{x}{2}) = \frac{3}{3}

sec (x) csc (x) + 2 csc (x) = 0

sin (x) + 3 cos (x) = 1

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

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