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desarrollar (sin^2(x)(1+cos(x)))/(1-cos(x))

Solución

desarrollar

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

1 + 2 cos (x) + cos^{2} (x)

Pasos de solución

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

Expandir

sin^{2} (x) (1 + cos (x)) : sin^{2} (x) + sin^{2} (x) cos (x)

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

Simplificar

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

= \frac{\frac{1 + c o s ( x )}{c s c ^{2} ( x )}}{1 - cos ( x )}

Aplicar las propiedades de las fracciones:

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

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

Simplificar

csc^{2} (x) (- cos (x) + 1) : \frac{1}{cos ( x ) + 1}

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

Aplicar la regla

\frac{a}{1} = a

= (cos (x) + 1) (cos (x) + 1)

Aplicar las leyes de los exponentes:

a^{b} \cdot a^{c} = a^{b + c}

(1 + cos (x)) (1 + cos (x)) = (1 + cos (x))^{1 + 1}

= (1 + cos (x))^{1 + 1}

Sumar:

1 + 1 = 2

= (1 + cos (x))^{2}

Aplicar la formula del binomio al cuadrado:

(a + b)^{2} = a^{2} + 2 ab + b^{2}

a = 1, b = cos (x)

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

Simplificar

1^{2} + 2 \cdot 1 \cdot cos (x) + cos^{2} (x) : 1 + 2 cos (x) + cos^{2} (x)

= 1 + 2 cos (x) + cos^{2} (x)

\frac{- S ^{3} - S}{4 ( S ^{4} + S ^{2} + 4 )}

(x^{2} - x - e^{3 x})^{2}

(x + 2 x) (x - 2 x)

(e^{iπ x} - e^{- iπ x})^{2}

N (- 5, - 1)