What is expand (sin^2(α)(1+cos(α)))/(1-cos(α)) ?

The solution to expand (sin^2(α)(1+cos(α)))/(1-cos(α)) is 1+2cos(α)+cos^2(α)

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expand (sin^2(α)(1+cos(α)))/(1-cos(α))

expand

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

1 + 2 cos (α) + cos^{2} (α)

Solution steps

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

Expand

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

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

Simplify

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

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

Apply the fraction rule:

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

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

Simplify

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

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

Apply the fraction rule:

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

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

Apply rule

\frac{a}{1} = a

= (cos (α) + 1) (cos (α) + 1)

Apply exponent rule:

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

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

= (1 + cos (α))^{1 + 1}

Add the numbers:

1 + 1 = 2

= (1 + cos (α))^{2}

Apply Perfect Square Formula:

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

a = 1, b = cos (α)

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

Simplify

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

= 1 + 2 cos (α) + cos^{2} (α)

(3 x + 1 \circ \frac{1}{x + 2}) (2)

(- 10000 + 0.7 x cot (y))^{2}

2 (x - 2) (x + 13) (x - 13)

\frac{( - 6 + y ^{2} ) ^{2} y}{8}

\frac{x ( x + 1 ) d y}{d x}

What is expand (sin^2(α)(1+cos(α)))/(1-cos(α)) ?
The solution to expand (sin^2(α)(1+cos(α)))/(1-cos(α)) is 1+2cos(α)+cos^2(α)