solvefor x,cos(x)+cos(x+y)=0

Solución

resolver para

x, cos (x) + cos (x + y) = 0

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

Pasos de solución

cos (x) + cos (x + y) = 0

Re-escribir usando identidades trigonométricas

2 cos (- \frac{y}{2}) cos (\frac{2 x + y}{2}) = 0

Utilizando el teorema de factor cero: si

ab = 0

entonces

a = 0

b = 0

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

Soluciones generales para

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

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

Resolver

\frac{2 x + y}{2} = \frac{π}{2} + 2 πn : x = \frac{π}{2} + 2 πn - \frac{y}{2}

Resolver

\frac{2 x + y}{2} = \frac{3 π}{2} + 2 πn : x = \frac{3 π}{2} + 2 πn - \frac{y}{2}

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

cosh (x) = 1

- 2 sin (x) - 1 = 0

3 sin (θ) + cos (θ) = 1

3 csc (x) + 2 = 0

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