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Popular >

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

Solución

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

Solución

x = \frac{π}{2} + 2 πn

+1

Grados

x = 9 0^{\circ} + 36 0^{\circ} n

Pasos de solución

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

Re-escribir usando identidades trigonométricas

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

Dividir ambos lados entre

cos (\frac{x}{2}), cos (\frac{x}{2}) \neq = 0

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

Simplificar

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

Utilizar la identidad trigonométrica básica:

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

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

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

Mover

1

al lado derecho

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

Sumar

1

a ambos lados

tan (\frac{x}{2}) - 1 + 1 = 0 + 1

Simplificar

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

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

Soluciones generales para

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

tan (x)

tabla de valores periódicos con

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} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

\frac{x}{2} = \frac{π}{4} + πn

\frac{x}{2} = \frac{π}{4} + πn

Resolver

\frac{x}{2} = \frac{π}{4} + πn : x = \frac{π}{2} + 2 πn

\frac{x}{2} = \frac{π}{4} + πn

Multiplicar ambos lados por

2

\frac{x}{2} = \frac{π}{4} + πn

Multiplicar ambos lados por

2

\frac{2 x}{2} = 2 \cdot \frac{π}{4} + 2 πn

Simplificar

\frac{2 x}{2} = 2 \cdot \frac{π}{4} + 2 πn

Simplificar

\frac{2 x}{2} : x

\frac{2 x}{2}

Dividir:

\frac{2}{2} = 1

= x

Simplificar

2 \cdot \frac{π}{4} + 2 πn : \frac{π}{2} + 2 πn

2 \cdot \frac{π}{4} + 2 πn

2 \cdot \frac{π}{4} = \frac{π}{2}

2 \cdot \frac{π}{4}

Multiplicar fracciones:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{π 2}{4}

Eliminar los terminos comunes:

2

= \frac{π}{2}

= \frac{π}{2} + 2 πn

x = \frac{π}{2} + 2 πn

x = \frac{π}{2} + 2 πn

x = \frac{π}{2} + 2 πn

x = \frac{π}{2} + 2 πn

Ejemplos populares

2sin^2(x/3)=1,-pi<= ,x<= pi

2 sin^{2} (\frac{x}{3}) = 1, - π \leq, x \leq π

cos^2(x)+sin^2(x)=sin(x)+1/2

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

sin (A) = 0.53

tan(a)=sqrt(3),cos(a)

tan (a) = 3, cos (a)

2sin(2x)=cos(2x)

2 sin (2 x) = cos (2 x)