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受欢迎的三角函数 >

4/(tan(36))

解答

\frac{4}{tan ( 3 6 ^{\circ} )}

解答

\frac{( 5 2 + 3 10 ) 5 - 5}{5}

+1

十进制

5.50552 \dots

求解步骤

\frac{4}{tan ( 3 6 ^{\circ} )}

使用三角恒等式改写:

tan (3 6^{\circ}) = \frac{2 ( 5 - 1 ) 5 - 5}{4}

tan (3 6^{\circ})

使用三角恒等式改写:

\frac{sin ( 3 6 ^{\circ} )}{cos ( 3 6 ^{\circ} )}

tan (3 6^{\circ})

使用基本三角恒等式:

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

= \frac{sin ( 3 6 ^{\circ} )}{cos ( 3 6 ^{\circ} )}

= \frac{sin ( 3 6 ^{\circ} )}{cos ( 3 6 ^{\circ} )}

使用三角恒等式改写:

sin (3 6^{\circ}) = \frac{2 5 - 5}{4}

sin (3 6^{\circ})

显示:

cos (3 6^{\circ}) - sin (1 8^{\circ}) = \frac{1}{2}

使用以下积化和差公式:

2 sin (x) cos (y) = sin (x + y) - sin (x - y)

2 cos (3 6^{\circ}) sin (1 8^{\circ}) = sin (5 4^{\circ}) - sin (1 8^{\circ})

显示:

2 cos (3 6^{\circ}) sin (1 8^{\circ}) = \frac{1}{2}

使用倍角公式:

sin (2 x) = 2 sin (x) cos (x)

sin (7 2^{\circ}) = 2 sin (3 6^{\circ}) cos (3 6^{\circ})

sin (7 2^{\circ}) sin (3 6^{\circ}) = 4 sin (3 6^{\circ}) sin (1 8^{\circ}) cos (3 6^{\circ}) cos (1 8^{\circ})

两边除以

sin (3 6^{\circ})

sin (7 2^{\circ}) = 4 sin (1 8^{\circ}) cos (3 6^{\circ}) cos (1 8^{\circ})

利用以下特性:

sin (x) = cos (9 0^{\circ} - x)

sin (7 2^{\circ}) = cos (9 0^{\circ} - 7 2^{\circ})

cos (9 0^{\circ} - 7 2^{\circ}) = 4 sin (1 8^{\circ}) cos (3 6^{\circ}) cos (1 8^{\circ})

cos (1 8^{\circ}) = 4 sin (1 8^{\circ}) cos (3 6^{\circ}) cos (1 8^{\circ})

两边除以

cos (1 8^{\circ})

1 = 4 sin (1 8^{\circ}) cos (3 6^{\circ})

两边除以

2

\frac{1}{2} = 2 sin (1 8^{\circ}) cos (3 6^{\circ})

代入

\frac{1}{2} = 2 sin (1 8^{\circ}) cos (3 6^{\circ})

\frac{1}{2} = sin (5 4^{\circ}) - sin (1 8^{\circ})

sin (5 4^{\circ}) = cos (9 0^{\circ} - 5 4^{\circ})

\frac{1}{2} = cos (9 0^{\circ} - 5 4^{\circ}) - sin (1 8^{\circ})

\frac{1}{2} = cos (3 6^{\circ}) - sin (1 8^{\circ})

显示:

cos (3 6^{\circ}) + sin (1 8^{\circ}) = \frac{5}{4}

使用因式分解法则:

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

a = cos (3 6^{\circ}) + sin (1 8^{\circ})

(cos (3 6^{\circ}) + sin (1 8^{\circ}))^{2} - (cos (3 6^{\circ}) - sin (1 8^{\circ}))^{2} = ((cos (3 6^{\circ}) + sin (1 8^{\circ})) + (cos (3 6^{\circ}) - sin (1 8^{\circ}))) ((cos (3 6^{\circ}) + sin (1 8^{\circ})) - (cos (3 6^{\circ}) - sin (1 8^{\circ})))

整理后得

(cos (3 6^{\circ}) + sin (1 8^{\circ}))^{2} - (cos (3 6^{\circ}) - sin (1 8^{\circ}))^{2} = 2 (2 cos (3 6^{\circ}) sin (1 8^{\circ}))

显示:

2 cos (3 6^{\circ}) sin (1 8^{\circ}) = \frac{1}{2}

使用倍角公式:

sin (2 x) = 2 sin (x) cos (x)

sin (7 2^{\circ}) = 2 sin (3 6^{\circ}) cos (3 6^{\circ})

sin (7 2^{\circ}) sin (3 6^{\circ}) = 4 sin (3 6^{\circ}) sin (1 8^{\circ}) cos (3 6^{\circ}) cos (1 8^{\circ})

两边除以

sin (3 6^{\circ})

sin (7 2^{\circ}) = 4 sin (1 8^{\circ}) cos (3 6^{\circ}) cos (1 8^{\circ})

利用以下特性:

sin (x) = cos (9 0^{\circ} - x)

sin (7 2^{\circ}) = cos (9 0^{\circ} - 7 2^{\circ})

cos (9 0^{\circ} - 7 2^{\circ}) = 4 sin (1 8^{\circ}) cos (3 6^{\circ}) cos (1 8^{\circ})

cos (1 8^{\circ}) = 4 sin (1 8^{\circ}) cos (3 6^{\circ}) cos (1 8^{\circ})

两边除以

cos (1 8^{\circ})

1 = 4 sin (1 8^{\circ}) cos (3 6^{\circ})

两边除以

2

\frac{1}{2} = 2 sin (1 8^{\circ}) cos (3 6^{\circ})

代入

2 cos (3 6^{\circ}) sin (1 8^{\circ}) = \frac{1}{2}

(cos (3 6^{\circ}) + sin (1 8^{\circ}))^{2} - (cos (3 6^{\circ}) - sin (1 8^{\circ}))^{2} = 1

代入

cos (3 6^{\circ}) - sin (1 8^{\circ}) = \frac{1}{2}

(cos (3 6^{\circ}) + sin (1 8^{\circ}))^{2} - (\frac{1}{2})^{2} = 1

整理后得

(cos (3 6^{\circ}) + sin (1 8^{\circ}))^{2} - \frac{1}{4} = 1

两边加上

\frac{1}{4}

(cos (3 6^{\circ}) + sin (1 8^{\circ}))^{2} - \frac{1}{4} + \frac{1}{4} = 1 + \frac{1}{4}

整理后得

(cos (3 6^{\circ}) + sin (1 8^{\circ}))^{2} = \frac{5}{4}

在两侧开平方

cos (3 6^{\circ}) + sin (1 8^{\circ}) = \pm \frac{5}{4}

cos (3 6^{\circ})

不能为负

sin (1 8^{\circ})

不能为负

cos (3 6^{\circ}) + sin (1 8^{\circ}) = \frac{5}{4}

以下方程式相加

cos (3 6^{\circ}) + sin (1 8^{\circ}) = \frac{5}{2}

((cos (3 6^{\circ}) + sin (1 8^{\circ})) + (cos (3 6^{\circ}) - sin (1 8^{\circ}))) = (\frac{5}{2} + \frac{1}{2})

整理后得

cos (3 6^{\circ}) = \frac{5 + 1}{4}

两边进行平方

(cos (3 6^{\circ}))^{2} = (\frac{5 + 1}{4})^{2}

利用以下特性:

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

sin^{2} (3 6^{\circ}) = 1 - cos^{2} (3 6^{\circ})

代入

cos (3 6^{\circ}) = \frac{5 + 1}{4}

sin^{2} (3 6^{\circ}) = 1 - (\frac{5 + 1}{4})^{2}

整理后得

sin^{2} (3 6^{\circ}) = \frac{5 - 5}{8}

在两侧开平方

sin (3 6^{\circ}) = \pm \frac{5 - 5}{8}

sin (3 6^{\circ})

不能为负

sin (3 6^{\circ}) = \frac{5 - 5}{8}

整理后得

sin (3 6^{\circ}) = \frac{\frac{5 - 5}{2}}{2}

= \frac{\frac{5 - 5}{2}}{2}

化简

= \frac{2 5 - 5}{4}

使用三角恒等式改写:

cos (3 6^{\circ}) = \frac{5 + 1}{4}

cos (3 6^{\circ})

显示:

cos (3 6^{\circ}) - sin (1 8^{\circ}) = \frac{1}{2}

使用以下积化和差公式:

2 sin (x) cos (y) = sin (x + y) - sin (x - y)

2 cos (3 6^{\circ}) sin (1 8^{\circ}) = sin (5 4^{\circ}) - sin (1 8^{\circ})

显示:

2 cos (3 6^{\circ}) sin (1 8^{\circ}) = \frac{1}{2}

使用倍角公式:

sin (2 x) = 2 sin (x) cos (x)

sin (7 2^{\circ}) = 2 sin (3 6^{\circ}) cos (3 6^{\circ})

sin (7 2^{\circ}) sin (3 6^{\circ}) = 4 sin (3 6^{\circ}) sin (1 8^{\circ}) cos (3 6^{\circ}) cos (1 8^{\circ})

两边除以

sin (3 6^{\circ})

sin (7 2^{\circ}) = 4 sin (1 8^{\circ}) cos (3 6^{\circ}) cos (1 8^{\circ})

利用以下特性:

sin (x) = cos (9 0^{\circ} - x)

sin (7 2^{\circ}) = cos (9 0^{\circ} - 7 2^{\circ})

cos (9 0^{\circ} - 7 2^{\circ}) = 4 sin (1 8^{\circ}) cos (3 6^{\circ}) cos (1 8^{\circ})

cos (1 8^{\circ}) = 4 sin (1 8^{\circ}) cos (3 6^{\circ}) cos (1 8^{\circ})

两边除以

cos (1 8^{\circ})

1 = 4 sin (1 8^{\circ}) cos (3 6^{\circ})

两边除以

2

\frac{1}{2} = 2 sin (1 8^{\circ}) cos (3 6^{\circ})

代入

\frac{1}{2} = 2 sin (1 8^{\circ}) cos (3 6^{\circ})

\frac{1}{2} = sin (5 4^{\circ}) - sin (1 8^{\circ})

sin (5 4^{\circ}) = cos (9 0^{\circ} - 5 4^{\circ})

\frac{1}{2} = cos (9 0^{\circ} - 5 4^{\circ}) - sin (1 8^{\circ})

\frac{1}{2} = cos (3 6^{\circ}) - sin (1 8^{\circ})

显示:

cos (3 6^{\circ}) + sin (1 8^{\circ}) = \frac{5}{4}

使用因式分解法则:

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

a = cos (3 6^{\circ}) + sin (1 8^{\circ})

(cos (3 6^{\circ}) + sin (1 8^{\circ}))^{2} - (cos (3 6^{\circ}) - sin (1 8^{\circ}))^{2} = ((cos (3 6^{\circ}) + sin (1 8^{\circ})) + (cos (3 6^{\circ}) - sin (1 8^{\circ}))) ((cos (3 6^{\circ}) + sin (1 8^{\circ})) - (cos (3 6^{\circ}) - sin (1 8^{\circ})))

整理后得

(cos (3 6^{\circ}) + sin (1 8^{\circ}))^{2} - (cos (3 6^{\circ}) - sin (1 8^{\circ}))^{2} = 2 (2 cos (3 6^{\circ}) sin (1 8^{\circ}))

显示:

2 cos (3 6^{\circ}) sin (1 8^{\circ}) = \frac{1}{2}

使用倍角公式:

sin (2 x) = 2 sin (x) cos (x)

sin (7 2^{\circ}) = 2 sin (3 6^{\circ}) cos (3 6^{\circ})

sin (7 2^{\circ}) sin (3 6^{\circ}) = 4 sin (3 6^{\circ}) sin (1 8^{\circ}) cos (3 6^{\circ}) cos (1 8^{\circ})

两边除以

sin (3 6^{\circ})

sin (7 2^{\circ}) = 4 sin (1 8^{\circ}) cos (3 6^{\circ}) cos (1 8^{\circ})

利用以下特性:

sin (x) = cos (9 0^{\circ} - x)

sin (7 2^{\circ}) = cos (9 0^{\circ} - 7 2^{\circ})

cos (9 0^{\circ} - 7 2^{\circ}) = 4 sin (1 8^{\circ}) cos (3 6^{\circ}) cos (1 8^{\circ})

cos (1 8^{\circ}) = 4 sin (1 8^{\circ}) cos (3 6^{\circ}) cos (1 8^{\circ})

两边除以

cos (1 8^{\circ})

1 = 4 sin (1 8^{\circ}) cos (3 6^{\circ})

两边除以

2

\frac{1}{2} = 2 sin (1 8^{\circ}) cos (3 6^{\circ})

代入

2 cos (3 6^{\circ}) sin (1 8^{\circ}) = \frac{1}{2}

(cos (3 6^{\circ}) + sin (1 8^{\circ}))^{2} - (cos (3 6^{\circ}) - sin (1 8^{\circ}))^{2} = 1

代入

cos (3 6^{\circ}) - sin (1 8^{\circ}) = \frac{1}{2}

(cos (3 6^{\circ}) + sin (1 8^{\circ}))^{2} - (\frac{1}{2})^{2} = 1

整理后得

(cos (3 6^{\circ}) + sin (1 8^{\circ}))^{2} - \frac{1}{4} = 1

两边加上

\frac{1}{4}

(cos (3 6^{\circ}) + sin (1 8^{\circ}))^{2} - \frac{1}{4} + \frac{1}{4} = 1 + \frac{1}{4}

整理后得

(cos (3 6^{\circ}) + sin (1 8^{\circ}))^{2} = \frac{5}{4}

在两侧开平方

cos (3 6^{\circ}) + sin (1 8^{\circ}) = \pm \frac{5}{4}

cos (3 6^{\circ})

不能为负

sin (1 8^{\circ})

不能为负

cos (3 6^{\circ}) + sin (1 8^{\circ}) = \frac{5}{4}

以下方程式相加

cos (3 6^{\circ}) + sin (1 8^{\circ}) = \frac{5}{2}

((cos (3 6^{\circ}) + sin (1 8^{\circ})) + (cos (3 6^{\circ}) - sin (1 8^{\circ}))) = (\frac{5}{2} + \frac{1}{2})

整理后得

cos (3 6^{\circ}) = \frac{5 + 1}{4}

= \frac{5 + 1}{4}

= \frac{\frac{2 5 - 5}{4}}{\frac{5 + 1}{4}}

化简

\frac{\frac{2 5 - 5}{4}}{\frac{5 + 1}{4}} : \frac{2 ( 5 - 1 ) 5 - 5}{4}

\frac{\frac{2 5 - 5}{4}}{\frac{5 + 1}{4}}

分式相除:

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

= \frac{2 5 - 5 \cdot 4}{4 ( 5 + 1 )}

约分:

4

= \frac{2 5 - 5}{5 + 1}

\frac{2 5 - 5}{5 + 1}

有理化:

\frac{2 ( 5 - 1 ) 5 - 5}{4}

\frac{2 5 - 5}{5 + 1}

乘以共轭根式

\frac{5 - 1}{5 - 1}

= \frac{2 5 - 5 ( 5 - 1 )}{( 5 + 1 ) ( 5 - 1 )}

(5 + 1) (5 - 1) = 4

(5 + 1) (5 - 1)

使用平方差公式:

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

a = 5, b = 1

= (5)^{2} - 1^{2}

化简

(5)^{2} - 1^{2} : 4

(5)^{2} - 1^{2}

使用法则

1^{a} = 1

1^{2} = 1

= (5)^{2} - 1

(5)^{2} = 5

(5)^{2}

使用根式运算法则:

a = a^{\frac{1}{2}}

= (5^{\frac{1}{2}})^{2}

使用指数法则:

(a^{b})^{c} = a^{b c}

= 5^{\frac{1}{2} \cdot 2}

\frac{1}{2} \cdot 2 = 1

\frac{1}{2} \cdot 2

分式相乘:

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

= \frac{1 \cdot 2}{2}

约分:

2

= 1

= 5

= 5 - 1

数字相减:

5 - 1 = 4

= 4

= 4

= \frac{2 ( 5 - 1 ) 5 - 5}{4}

= \frac{2 ( 5 - 1 ) 5 - 5}{4}

= \frac{2 ( 5 - 1 ) 5 - 5}{4}

= \frac{4}{\frac{2 ( 5 - 1 ) 5 - 5}{4}}

化简

\frac{4}{\frac{2 ( 5 - 1 ) 5 - 5}{4}} : \frac{( 5 2 + 3 10 ) 5 - 5}{5}

\frac{4}{\frac{2 ( 5 - 1 ) 5 - 5}{4}}

使用分式法则:

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

= \frac{4 \cdot 4}{2 ( 5 - 1 ) 5 - 5}

数字相乘:

4 \cdot 4 = 16

= \frac{16}{2 ( 5 - 1 ) 5 - 5}

分解

16 : 2^{4}

因式分解

16 = 2^{4}

= \frac{2 ^{4}}{2 ( 5 - 1 ) 5 - 5}

消掉

\frac{2 ^{4}}{2 ( 5 - 1 ) 5 - 5} : \frac{2 ^{\frac{7}{2}}}{( 5 - 1 ) 5 - 5}

\frac{2 ^{4}}{2 ( 5 - 1 ) 5 - 5}

使用根式运算法则:

n a = a^{\frac{1}{n}}

2 = 2^{\frac{1}{2}}

= \frac{2 ^{4}}{2 ^{\frac{1}{2}} ( 5 - 1 ) 5 - 5}

使用指数法则:

\frac{x ^{a}}{x ^{b}} = x^{a - b}

\frac{2 ^{4}}{2 ^{\frac{1}{2}}} = 2^{4 - \frac{1}{2}}

= \frac{2 ^{4 - \frac{1}{2}}}{( 5 - 1 ) 5 - 5}

数字相减:

4 - \frac{1}{2} = \frac{7}{2}

= \frac{2 ^{\frac{7}{2}}}{( 5 - 1 ) 5 - 5}

= \frac{2 ^{\frac{7}{2}}}{( 5 - 1 ) 5 - 5}

2^{\frac{7}{2}} = 2^{3} 2

2^{\frac{7}{2}}

2^{\frac{7}{2}} = 2^{3 + \frac{1}{2}}

= 2^{3 + \frac{1}{2}}

使用指数法则:

x^{a + b} = x^{a} x^{b}

= 2^{3} \cdot 2^{\frac{1}{2}}

整理后得

= 2^{3} 2

= \frac{2 ^{3} 2}{( 5 - 1 ) 5 - 5}

2^{3} = 8

= \frac{8 2}{( 5 - 1 ) 5 - 5}

\frac{8 2}{( 5 - 1 ) 5 - 5}

有理化:

\frac{( 5 2 + 3 10 ) 5 - 5}{5}

\frac{8 2}{( 5 - 1 ) 5 - 5}

乘以共轭根式

\frac{5 + 1}{5 + 1}

= \frac{8 2 ( 5 + 1 )}{( 5 - 1 ) 5 - 5 ( 5 + 1 )}

(5 - 1) 5 - 5 (5 + 1) = 4 5 - 5

(5 - 1) 5 - 5 (5 + 1)

= (5 - 1) (5 + 1) 5 - 5

乘开

(5 - 1) (5 + 1) : 4

(5 - 1) (5 + 1)

使用平方差公式:

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

a = 5, b = 1

= (5)^{2} - 1^{2}

化简

(5)^{2} - 1^{2} : 4

(5)^{2} - 1^{2}

使用法则

1^{a} = 1

1^{2} = 1

= (5)^{2} - 1

(5)^{2} = 5

(5)^{2}

使用根式运算法则:

a = a^{\frac{1}{2}}

= (5^{\frac{1}{2}})^{2}

使用指数法则:

(a^{b})^{c} = a^{b c}

= 5^{\frac{1}{2} \cdot 2}

\frac{1}{2} \cdot 2 = 1

\frac{1}{2} \cdot 2

分式相乘:

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

= \frac{1 \cdot 2}{2}

约分:

2

= 1

= 5

= 5 - 1

数字相减:

5 - 1 = 4

= 4

= 4

= 5 - 5 \cdot 4

乘开

5 - 5 \cdot 4 : 4 5 - 5

5 - 5 \cdot 4

打开括号

= 5 - 5 \cdot 4

= 4 5 - 5

= 4 5 - 5

= \frac{8 2 ( 5 + 1 )}{4 5 - 5}

数字相除:

\frac{8}{4} = 2

= \frac{2 2 ( 1 + 5 )}{5 - 5}

乘以共轭根式

\frac{5 - 5}{5 - 5}

= \frac{2 2 ( 1 + 5 ) 5 - 5}{5 - 5 5 - 5}

5 - 5 5 - 5 = 5 - 5

5 - 5 5 - 5

使用根式运算法则:

a a = a

5 - 5 5 - 5 = 5 - 5

= 5 - 5

= \frac{2 2 ( 1 + 5 ) 5 - 5}{5 - 5}

乘以共轭根式

\frac{5 + 5}{5 + 5}

= \frac{2 2 ( 1 + 5 ) 5 - 5 ( 5 + 5 )}{( 5 - 5 ) ( 5 + 5 )}

22 (1 + 5) 5 - 5 (5 + 5) = 202 5 - 5 + 1210 5 - 5

22 (1 + 5) 5 - 5 (5 + 5)

= 22 (1 + 5) (5 + 5) 5 - 5

乘开

(1 + 5) (5 + 5) : 10 + 65

(1 + 5) (5 + 5)

使用 FOIL 方法:

(a + b) (c + d) = a c + a d + b c + b d

a = 1, b = 5, c = 5, d = 5

= 1 \cdot 5 + 1 \cdot 5 + 5 \cdot 5 + 55

= 1 \cdot 5 + 1 \cdot 5 + 55 + 55

化简

1 \cdot 5 + 1 \cdot 5 + 55 + 55 : 10 + 65

1 \cdot 5 + 1 \cdot 5 + 55 + 55

同类项相加:

1 \cdot 5 + 55 = 65

= 1 \cdot 5 + 65 + 55

数字相乘:

1 \cdot 5 = 5

= 5 + 65 + 55

使用根式运算法则:

a a = a

55 = 5

= 5 + 65 + 5

数字相加:

5 + 5 = 10

= 10 + 65

= 10 + 65

= 22 5 - 5 (10 + 65)

乘开

22 5 - 5 (10 + 65) : 202 5 - 5 + 1210 5 - 5

22 5 - 5 (10 + 65)

使用分配律:

a (b + c) = ab + a c

a = 22 5 - 5, b = 10, c = 65

= 22 5 - 5 \cdot 10 + 22 5 - 5 \cdot 65

= 2 \cdot 102 5 - 5 + 2 \cdot 625 5 - 5

化简

2 \cdot 102 5 - 5 + 2 \cdot 625 5 - 5 : 202 5 - 5 + 1210 5 - 5

2 \cdot 102 5 - 5 + 2 \cdot 625 5 - 5

2 \cdot 102 5 - 5 = 202 5 - 5

2 \cdot 102 5 - 5

数字相乘:

2 \cdot 10 = 20

= 202 5 - 5

2 \cdot 625 5 - 5 = 1210 5 - 5

2 \cdot 625 5 - 5

数字相乘:

2 \cdot 6 = 12

= 1225 5 - 5

使用根式运算法则:

a b = a \cdot b

25 5 - 5 = 2 \cdot 5 (5 - 5)

= 12 2 \cdot 5 (5 - 5)

数字相乘:

2 \cdot 5 = 10

= 12 10 (5 - 5)

使用根式运算法则:

n ab = n a n b,

假定

a \geq 0, b \geq 0

10 (5 - 5) = 10 5 - 5

= 1210 5 - 5

= 202 5 - 5 + 1210 5 - 5

= 202 5 - 5 + 1210 5 - 5

= 202 5 - 5 + 1210 5 - 5

(5 - 5) (5 + 5) = 20

(5 - 5) (5 + 5)

使用平方差公式:

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

a = 5, b = 5

= 5^{2} - (5)^{2}

化简

5^{2} - (5)^{2} : 20

5^{2} - (5)^{2}

5^{2} = 25

5^{2}

5^{2} = 25

= 25

(5)^{2} = 5

(5)^{2}

使用根式运算法则:

a = a^{\frac{1}{2}}

= (5^{\frac{1}{2}})^{2}

使用指数法则:

(a^{b})^{c} = a^{b c}

= 5^{\frac{1}{2} \cdot 2}

\frac{1}{2} \cdot 2 = 1

\frac{1}{2} \cdot 2

分式相乘:

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

= \frac{1 \cdot 2}{2}

约分:

2

= 1

= 5

= 25 - 5

数字相减:

25 - 5 = 20

= 20

= 20

= \frac{20 2 5 - 5 + 12 10 5 - 5}{20}

分解

202 5 - 5 + 1210 5 - 5 : 4 5 - 5 (52 + 310)

202 5 - 5 + 1210 5 - 5

改写为

= 5 \cdot 4 5 - 5 2 + 3 \cdot 4 5 - 5 10

因式分解出通项

4 5 - 5

= 4 5 - 5 (52 + 310)

= \frac{4 5 - 5 ( 5 2 + 3 10 )}{20}

约分:

4

= \frac{( 5 2 + 3 10 ) 5 - 5}{5}

= \frac{( 5 2 + 3 10 ) 5 - 5}{5}

= \frac{( 5 2 + 3 10 ) 5 - 5}{5}

流行的例子

sin (4 (0))

cos (3 0^{\circ}) \cdot 15

arcsin (- 0.8)

\frac{20}{tan ( 4 0 ^{\circ} )}

- 2 cos (\frac{7 π}{6})