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受欢迎的代数 >

展开 (sin^2(α)(1+cos(α)))/(1-cos(α))

解答

展开

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

解答

1 + 2 cos (α) + cos^{2} (α)

求解步骤

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

乘开

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 )}

化简

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 )}

使用分式法则:

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

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

化简

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

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

使用分式法则:

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

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

使用法则

\frac{a}{1} = a

= (cos (α) + 1) (cos (α) + 1)

使用指数法则:

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

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

= (1 + cos (α))^{1 + 1}

数字相加:

1 + 1 = 2

= (1 + cos (α))^{2}

使用完全平方公式:

(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)

化简

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)

流行的例子

化简 (3x+1\circ 1/(sqrt(x+2)))(2)

s im pl i f y (3 x + 1 \circ \frac{1}{x + 2}) (2)

展开 (-10000+0.7xcot(y))^2

e x p an d (- 10000 + 0.7 x cot (y))^{2}

化简 2(x-2)(x+sqrt(13))(x-sqrt(13))

s im pl i f y 2 (x - 2) (x + 13) (x - 13)

展开 ((-6+y^2)^2y)/8

e x p an d \frac{( - 6 + y ^{2} ) ^{2} y}{8}

展开 (x(x+1)dy)/(dx)

e x p an d \frac{x ( x + 1 ) d y}{d x}