zs

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

受欢迎的三角函数 >

arctan(x+2)=arcsin(7/25)+arccos(4/5)

解答

arctan (x + 2) = arcsin (\frac{7}{25}) + arccos (\frac{4}{5})

解答

x = - \frac{2}{3}

求解步骤

arctan (x + 2) = arcsin (\frac{7}{25}) + arccos (\frac{4}{5})

使用反三角函数性质

arctan (x + 2) = arcsin (\frac{7}{25}) + arccos (\frac{4}{5})

arctan (x) = a \Rightarrow x = tan (a)

x + 2 = tan (arcsin (\frac{7}{25}) + arccos (\frac{4}{5}))

tan (arcsin (\frac{7}{25}) + arccos (\frac{4}{5})) = \frac{4}{3}

tan (arcsin (\frac{7}{25}) + arccos (\frac{4}{5}))

使用三角恒等式改写:

\frac{tan ( arcsin ( \frac{7}{25} ) ) + tan ( arccos ( \frac{4}{5} ) )}{1 - tan ( arcsin ( \frac{7}{25} ) ) tan ( arccos ( \frac{4}{5} ) )}

tan (arcsin (\frac{7}{25}) + arccos (\frac{4}{5}))

使用角和恒等式:

tan (s + t) = \frac{tan ( s ) + tan ( t )}{1 - tan ( s ) tan ( t )}

= \frac{tan ( arcsin ( \frac{7}{25} ) ) + tan ( arccos ( \frac{4}{5} ) )}{1 - tan ( arcsin ( \frac{7}{25} ) ) tan ( arccos ( \frac{4}{5} ) )}

= \frac{tan ( arcsin ( \frac{7}{25} ) ) + tan ( arccos ( \frac{4}{5} ) )}{1 - tan ( arcsin ( \frac{7}{25} ) ) tan ( arccos ( \frac{4}{5} ) )}

使用三角恒等式改写:

tan (arcsin (\frac{7}{25})) = \frac{7}{24}

tan (arcsin (\frac{7}{25}))

使用三角恒等式改写:

tan (arcsin (\frac{7}{25})) = \frac{( \frac{7}{25} ) 1 - ( \frac{7}{25} ) ^{2}}{1 - ( \frac{7}{25} ) ^{2}}

利用以下特性:

tan (arcsin (x)) = \frac{x 1 - x ^{2}}{1 - x ^{2}}

= \frac{( \frac{7}{25} ) 1 - ( \frac{7}{25} ) ^{2}}{1 - ( \frac{7}{25} ) ^{2}}

= \frac{\frac{7}{25} 1 - ( \frac{7}{25} ) ^{2}}{1 - ( \frac{7}{25} ) ^{2}}

化简

= \frac{7}{24}

使用三角恒等式改写:

tan (arccos (\frac{4}{5})) = \frac{3}{4}

tan (arccos (\frac{4}{5}))

使用三角恒等式改写:

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

利用以下特性:

tan (arccos (x)) = \frac{1 - x ^{2}}{x}

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

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

化简

= \frac{3}{4}

= \frac{\frac{7}{24} + \frac{3}{4}}{1 - \frac{7}{24} \cdot \frac{3}{4}}

化简

\frac{\frac{7}{24} + \frac{3}{4}}{1 - \frac{7}{24} \cdot \frac{3}{4}} : \frac{4}{3}

\frac{\frac{7}{24} + \frac{3}{4}}{1 - \frac{7}{24} \cdot \frac{3}{4}}

\frac{7}{24} \cdot \frac{3}{4} = \frac{7}{32}

\frac{7}{24} \cdot \frac{3}{4}

交叉约去公约数:

3

3, 24

最大公约数 (GCD)

3

质因数分解:

3

3

3

是质数，因此无法因数分解

= 3

24

质因数分解:

2 \cdot 2 \cdot 2 \cdot 3

24

24

除以

224 = 12 \cdot 2

= 2 \cdot 12

12

除以

212 = 6 \cdot 2

= 2 \cdot 2 \cdot 6

6

除以

26 = 3 \cdot 2

= 2 \cdot 2 \cdot 2 \cdot 3

2, 3

都是质数，因此无法进一步因数分解

= 2 \cdot 2 \cdot 2 \cdot 3

3, 24

的共同质因数是

= 3

= \frac{7}{8} \cdot \frac{1}{4}

分式相乘:

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

= \frac{7 \cdot 1}{8 \cdot 4}

数字相乘:

7 \cdot 1 = 7

= \frac{7}{8 \cdot 4}

数字相乘:

8 \cdot 4 = 32

= \frac{7}{32}

= \frac{\frac{7}{24} + \frac{3}{4}}{1 - \frac{7}{32}}

化简

\frac{7}{24} + \frac{3}{4} : \frac{25}{24}

\frac{7}{24} + \frac{3}{4}

24, 4

的最小公倍数:

24

24, 4

最小公倍数 (LCM)

24

质因数分解:

2 \cdot 2 \cdot 2 \cdot 3

24

24

除以

224 = 12 \cdot 2

= 2 \cdot 12

12

除以

212 = 6 \cdot 2

= 2 \cdot 2 \cdot 6

6

除以

26 = 3 \cdot 2

= 2 \cdot 2 \cdot 2 \cdot 3

2, 3

都是质数，因此无法进一步因数分解

= 2 \cdot 2 \cdot 2 \cdot 3

4

质因数分解:

2 \cdot 2

4

4

除以

24 = 2 \cdot 2

= 2 \cdot 2

将每个因子乘以它在

24

或

4

中出现的最多次数

= 2 \cdot 2 \cdot 2 \cdot 3

数字相乘:

2 \cdot 2 \cdot 2 \cdot 3 = 24

= 24

根据最小公倍数调整分式

将每个分子乘以其分母转变为最小公倍数所要乘以的同一数值

24

对于

\frac{3}{4} :

将分母和分子乘以

6

\frac{3}{4} = \frac{3 \cdot 6}{4 \cdot 6} = \frac{18}{24}

= \frac{7}{24} + \frac{18}{24}

因为分母相等，所以合并分式:

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

= \frac{7 + 18}{24}

数字相加:

7 + 18 = 25

= \frac{25}{24}

= \frac{\frac{25}{24}}{1 - \frac{7}{32}}

使用分式法则:

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

= \frac{25}{24 ( 1 - \frac{7}{32} )}

化简

1 - \frac{7}{32} : \frac{25}{32}

1 - \frac{7}{32}

将项转换为分式:

1 = \frac{1 \cdot 32}{32}

= \frac{1 \cdot 32}{32} - \frac{7}{32}

因为分母相等，所以合并分式:

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

= \frac{1 \cdot 32 - 7}{32}

1 \cdot 32 - 7 = 25

1 \cdot 32 - 7

数字相乘:

1 \cdot 32 = 32

= 32 - 7

数字相减:

32 - 7 = 25

= 25

= \frac{25}{32}

= \frac{25}{24 \cdot \frac{25}{32}}

乘

24 \cdot \frac{25}{32} : \frac{75}{4}

24 \cdot \frac{25}{32}

分式相乘:

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

= \frac{25 \cdot 24}{32}

数字相乘:

25 \cdot 24 = 600

= \frac{600}{32}

约分:

8

= \frac{75}{4}

= \frac{25}{\frac{75}{4}}

使用分式法则:

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

= \frac{25 \cdot 4}{75}

数字相乘:

25 \cdot 4 = 100

= \frac{100}{75}

约分:

25

= \frac{4}{3}

= \frac{4}{3}

x + 2 = \frac{4}{3}

x + 2 = \frac{4}{3}

解

x + 2 = \frac{4}{3} : x = - \frac{2}{3}

x + 2 = \frac{4}{3}

将

2

到右边

x + 2 = \frac{4}{3}

两边减去

2

x + 2 - 2 = \frac{4}{3} - 2

化简

x + 2 - 2 = \frac{4}{3} - 2

化简

x + 2 - 2 : x

x + 2 - 2

同类项相加:

2 - 2 = 0

= x

化简

\frac{4}{3} - 2 : - \frac{2}{3}

\frac{4}{3} - 2

将项转换为分式:

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

= - \frac{2 \cdot 3}{3} + \frac{4}{3}

因为分母相等，所以合并分式:

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

= \frac{- 2 \cdot 3 + 4}{3}

- 2 \cdot 3 + 4 = - 2

- 2 \cdot 3 + 4

数字相乘:

2 \cdot 3 = 6

= - 6 + 4

数字相加/相减:

- 6 + 4 = - 2

= - 2

= \frac{- 2}{3}

使用分式法则:

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

= - \frac{2}{3}

x = - \frac{2}{3}

x = - \frac{2}{3}

x = - \frac{2}{3}

x = - \frac{2}{3}

作图

流行的例子

(sec^2(a))cos^2(a)=sin^2(a)

-2sin(x)+5sin^2(x)=0

sqrt(3)*tan^2(x)-1=0