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Popular >

verificar sqrt(1+sin(2x))=sqrt(2)cos(x-45)

Solución

verificar

1 + sin (2 x) = 2 cos (x - 4 5^{\circ})

Solución

Falso

Pasos de solución

1 + sin (2 x) = 2 cos (x - 4 5^{\circ})

Ambos lados no son iguales

Multiplicar

1 + sin (2 x) = 2 cos (x - 4 5^{\circ})

por

x = 18 0^{\circ}

1 + sin (36 0^{\circ}) = 1

1 + sin (36 0^{\circ})

Re-escribir usando identidades trigonométricas:

sin (36 0^{\circ}) = 0

sin (36 0^{\circ})

sin (36 0^{\circ}) = sin (0)

sin (36 0^{\circ})

Reescribir

36 0^{\circ}

como

36 0^{\circ} + 0

= sin (36 0^{\circ} + 0)

Utilizar la periodicidad de

sin

sin (x + 36 0^{\circ}) = sin (x)

sin (36 0^{\circ} + 0) = sin (0)

= sin (0)

= sin (0)

Utilizar la siguiente identidad trivial:

sin (0) = 0

sin (0)

tabla de valores periódicos con

36 0^{\circ} n

intervalos:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= 0

= 0

= 1 + 0

Simplificar

= 1

2 cos (18 0^{\circ} - 4 5^{\circ}) = - 1

2 cos (18 0^{\circ} - 4 5^{\circ})

Re-escribir usando identidades trigonométricas:

cos (18 0^{\circ} - 4 5^{\circ}) = - \frac{2}{2}

cos (18 0^{\circ} - 4 5^{\circ})

Simplificar:

18 0^{\circ} - 4 5^{\circ} = 13 5^{\circ}

18 0^{\circ} - 4 5^{\circ}

Convertir a fracción:

18 0^{\circ} = 18 0^{\circ}

= 18 0^{\circ} - 4 5^{\circ}

Ya que los denominadores son iguales, combinar las fracciones:

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

= \frac{18 0 ^{\circ} 4 - 18 0 ^{\circ}}{4}

Sumar elementos similares:

72 0^{\circ} - 18 0^{\circ} = 54 0^{\circ}

= 13 5^{\circ}

= cos (13 5^{\circ})

Utilizar la siguiente identidad trivial:

cos (13 5^{\circ}) = - \frac{2}{2}

cos (13 5^{\circ})

cos (x)

tabla de valores periódicos con

36 0^{\circ} n

intervalos:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= - \frac{2}{2}

= - \frac{2}{2}

= 2 (- \frac{2}{2})

Simplificar

2 (- \frac{2}{2}) : - 1

2 (- \frac{2}{2})

Quitar los parentesis:

(- a) = - a

= - 2 \frac{2}{2}

Multiplicar fracciones:

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

= - \frac{2 2}{2}

22 = 2

22

Aplicar las leyes de los exponentes:

a a = a

22 = 2

= 2

= - \frac{2}{2}

Aplicar la regla

\frac{a}{a} = 1

= - 1

= - 1

Ambos lados no son iguales

\Rightarrow Falso

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