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verificar (1-cos(x))/(-1+1/(cos(x)))=cos(x)

Solución

verificar

\frac{1 - cos ( x )}{- 1 + \frac{1}{c o s ( x )}} = cos (x)

Verdadero

Pasos de solución

\frac{1 - cos ( x )}{- 1 + \frac{1}{c o s ( x )}} = cos (x)

Manipular el lado derecho

\frac{1 - cos ( x )}{- 1 + \frac{1}{c o s ( x )}}

Simplificar

\frac{1 - cos ( x )}{- 1 + \frac{1}{c o s ( x )}} : cos (x)

\frac{1 - cos ( x )}{- 1 + \frac{1}{c o s ( x )}}

Simplificar

- 1 + \frac{1}{cos ( x )}

en una fracción:

\frac{- cos ( x ) + 1}{cos ( x )}

- 1 + \frac{1}{cos ( x )}

Convertir a fracción:

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

= - \frac{1 \cdot cos ( x )}{cos ( x )} + \frac{1}{cos ( x )}

Ya que los denominadores son iguales, combinar las fracciones:

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

= \frac{- 1 \cdot cos ( x ) + 1}{cos ( x )}

Multiplicar:

1 \cdot cos (x) = cos (x)

= \frac{- cos ( x ) + 1}{cos ( x )}

= \frac{1 - cos ( x )}{\frac{- c o s ( x ) + 1}{c o s ( x )}}

Aplicar las propiedades de las fracciones:

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

= \frac{( 1 - cos ( x ) ) cos ( x )}{- cos ( x ) + 1}

Eliminar los terminos comunes:

1 - cos (x)

= cos (x)

= cos (x)

Se demostró que ambos lados pueden tomar la misma forma

\Rightarrow Verdadero

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

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

cos (a) = 2 cos^{2} (\frac{a}{2}) - 1

tan^{3} (x) = \frac{sin ^{3} ( x )}{cos ^{3} ( x )}

cos (4 θ) = 1 - 8 sin^{2} (θ) cos^{2} (θ)