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受欢迎的三角函数 >

arcsin(x)+arcsin(1-x)=arccos(x)

解答

arcsin (x) + arcsin (1 - x) = arccos (x)

解答

x = 0, x = \frac{1}{2}

求解步骤

arcsin (x) + arcsin (1 - x) = arccos (x)

a = b \Rightarrow cos (a) = cos (b)

cos (arcsin (x) + arcsin (1 - x)) = cos (arccos (x))

利用以下特性:

cos (s + t) = cos (s) cos (t) - sin (s) sin (t)

cos (arcsin (x)) cos (arcsin (1 - x)) - sin (arcsin (x)) sin (arcsin (1 - x)) = cos (arccos (x))

利用以下特性:

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

利用以下特性:

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

利用以下特性:

sin (arcsin (x)) = x

利用以下特性:

sin (arcsin (x)) = x

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

解

1 - x^{2} 1 - (1 - x)^{2} - x (1 - x) = x : x = 0, x = \frac{1}{2}

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

展开

1 - x^{2} 1 - (1 - x)^{2} - x (1 - x) : 1 - x^{2} - x^{2} + 2 x - x + x^{2}

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

乘开

- x (1 - x) : - x + x^{2}

- x (1 - x)

使用分配律:

a (b - c) = ab - a c

a = - x, b = 1, c = x

= - x \cdot 1 - (- x) x

使用加减运算法则

- (- a) = a

= - 1 \cdot x + xx

化简

- 1 \cdot x + xx : - x + x^{2}

- 1 \cdot x + xx

1 \cdot x = x

1 \cdot x

乘以:

1 \cdot x = x

= x

xx = x^{2}

xx

使用指数法则:

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

xx = x^{1 + 1}

= x^{1 + 1}

数字相加:

1 + 1 = 2

= x^{2}

= - x + x^{2}

= - x + x^{2}

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

展开

1 - x^{2} 1 - (1 - x)^{2} - x + x^{2} : 1 - x^{2} - x^{2} + 2 x - x + x^{2}

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

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

1 - (1 - x)^{2}

乘开

1 - (1 - x)^{2} : - x^{2} + 2 x

1 - (1 - x)^{2}

(1 - x)^{2} : 1 - 2 x + x^{2}

使用完全平方公式:

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

a = 1, b = x

= 1^{2} - 2 \cdot 1 \cdot x + x^{2}

化简

1^{2} - 2 \cdot 1 \cdot x + x^{2} : 1 - 2 x + x^{2}

1^{2} - 2 \cdot 1 \cdot x + x^{2}

使用法则

1^{a} = 1

1^{2} = 1

= 1 - 2 \cdot 1 \cdot x + x^{2}

数字相乘:

2 \cdot 1 = 2

= 1 - 2 x + x^{2}

= 1 - 2 x + x^{2}

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

- (1 - 2 x + x^{2}) : - 1 + 2 x - x^{2}

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

打开括号

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

使用加减运算法则

- (- a) = a, - (a) = - a

= - 1 + 2 x - x^{2}

= 1 - 1 + 2 x - x^{2}

1 - 1 = 0

= - x^{2} + 2 x

= - x^{2} + 2 x

= - x^{2} + 1 - x^{2} + 2 x - x + x^{2}

= 1 - x^{2} - x^{2} + 2 x - x + x^{2}

1 - x^{2} - x^{2} + 2 x - x + x^{2} = x

去除平方根

1 - x^{2} - x^{2} + 2 x - x + x^{2} = x

两边减去

- x + x^{2}

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

化简

1 - x^{2} - x^{2} + 2 x = 2 x - x^{2}

两边进行平方:

- x^{2} + 2 x + x^{4} - 2 x^{3} = 4 x^{2} - 4 x^{3} + x^{4}

1 - x^{2} - x^{2} + 2 x - x + x^{2} = x

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

展开

(1 - x^{2} - x^{2} + 2 x)^{2} : - x^{2} + 2 x + x^{4} - 2 x^{3}

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

使用指数法则:

(a \cdot b)^{n} = a^{n} b^{n}

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

(1 - x^{2})^{2} : 1 - x^{2}

使用根式运算法则:

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

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

使用指数法则:

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

= (1 - x^{2})^{\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

= 1 - x^{2}

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

(- x^{2} + 2 x)^{2} : - x^{2} + 2 x

使用根式运算法则:

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

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

使用指数法则:

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

= (- x^{2} + 2 x)^{\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

= - x^{2} + 2 x

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

展开

(1 - x^{2}) (- x^{2} + 2 x) : - x^{2} + 2 x + x^{4} - 2 x^{3}

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

使用 FOIL 方法:

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

a = 1, b = - x^{2}, c = - x^{2}, d = 2 x

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

使用加减运算法则

+ (- a) = - a, (- a) (- b) = ab

= - 1 \cdot x^{2} + 1 \cdot 2 x + x^{2} x^{2} - 2 x^{2} x

化简

- 1 \cdot x^{2} + 1 \cdot 2 x + x^{2} x^{2} - 2 x^{2} x : - x^{2} + 2 x + x^{4} - 2 x^{3}

- 1 \cdot x^{2} + 1 \cdot 2 x + x^{2} x^{2} - 2 x^{2} x

1 \cdot x^{2} = x^{2}

1 \cdot x^{2}

乘以:

1 \cdot x^{2} = x^{2}

= x^{2}

1 \cdot 2 x = 2 x

1 \cdot 2 x

数字相乘:

1 \cdot 2 = 2

= 2 x

x^{2} x^{2} = x^{4}

x^{2} x^{2}

使用指数法则:

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

x^{2} x^{2} = x^{2 + 2}

= x^{2 + 2}

数字相加:

2 + 2 = 4

= x^{4}

2 x^{2} x = 2 x^{3}

2 x^{2} x

使用指数法则:

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

x^{2} x = x^{2 + 1}

= 2 x^{2 + 1}

数字相加:

2 + 1 = 3

= 2 x^{3}

= - x^{2} + 2 x + x^{4} - 2 x^{3}

= - x^{2} + 2 x + x^{4} - 2 x^{3}

= - x^{2} + 2 x + x^{4} - 2 x^{3}

展开

(2 x - x^{2})^{2} : 4 x^{2} - 4 x^{3} + x^{4}

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

使用完全平方公式:

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

a = 2 x, b = x^{2}

= (2 x)^{2} - 2 \cdot 2 x x^{2} + (x^{2})^{2}

化简

(2 x)^{2} - 2 \cdot 2 x x^{2} + (x^{2})^{2} : 4 x^{2} - 4 x^{3} + x^{4}

(2 x)^{2} - 2 \cdot 2 x x^{2} + (x^{2})^{2}

(2 x)^{2} = 4 x^{2}

(2 x)^{2}

使用指数法则:

(a \cdot b)^{n} = a^{n} b^{n}

= 2^{2} x^{2}

2^{2} = 4

= 4 x^{2}

2 \cdot 2 x x^{2} = 4 x^{3}

2 \cdot 2 x x^{2}

数字相乘:

2 \cdot 2 = 4

= 4 x^{2} x

使用指数法则:

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

x x^{2} = x^{1 + 2}

= 4 x^{1 + 2}

数字相加:

1 + 2 = 3

= 4 x^{3}

(x^{2})^{2} = x^{4}

(x^{2})^{2}

使用指数法则:

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

= x^{2 \cdot 2}

数字相乘:

2 \cdot 2 = 4

= x^{4}

= 4 x^{2} - 4 x^{3} + x^{4}

= 4 x^{2} - 4 x^{3} + x^{4}

- x^{2} + 2 x + x^{4} - 2 x^{3} = 4 x^{2} - 4 x^{3} + x^{4}

- x^{2} + 2 x + x^{4} - 2 x^{3} = 4 x^{2} - 4 x^{3} + x^{4}

- x^{2} + 2 x + x^{4} - 2 x^{3} = 4 x^{2} - 4 x^{3} + x^{4}

解

- x^{2} + 2 x + x^{4} - 2 x^{3} = 4 x^{2} - 4 x^{3} + x^{4} : x = 0, x = \frac{1}{2}, x = 2

- x^{2} + 2 x + x^{4} - 2 x^{3} = 4 x^{2} - 4 x^{3} + x^{4}

两边减去

4 x^{2} - 4 x^{3} + x^{4}

- x^{2} + 2 x + x^{4} - 2 x^{3} - (4 x^{2} - 4 x^{3} + x^{4}) = 4 x^{2} - 4 x^{3} + x^{4} - (4 x^{2} - 4 x^{3} + x^{4})

化简

2 x^{3} - 5 x^{2} + 2 x = 0

因式分解

2 x^{3} - 5 x^{2} + 2 x : x (2 x - 1) (x - 2)

2 x^{3} - 5 x^{2} + 2 x

因式分解出通项

x : x (2 x^{2} - 5 x + 2)

2 x^{3} - 5 x^{2} + 2 x

使用指数法则:

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

x^{2} = xx

= 2 x^{2} x - 5 xx + 2 x

因式分解出通项

x

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

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

分解

2 x^{2} - 5 x + 2 : (2 x - 1) (x - 2)

2 x^{2} - 5 x + 2

将表达式拆分成组

2 x^{2} - 5 x + 2

定义

4

的因数:

1, 2, 4

4

约数 (因数)

找到

4

的质因数:

2, 2

4

4

除以

24 = 2 \cdot 2

= 2 \cdot 2

2

是质数，因此无法进一步因数分解

= 2 \cdot 2

添加质因数:

2

将 1 和数字

4

自身相加

1, 4

4

的因数

1, 2, 4

4

的负因数:

- 1, - 2, - 4

将因数乘以

- 1

得到负因数

- 1, - 2, - 4

对于每两个因数

u * v = 4

，检验是否

u + v = - 5

检验

u = 1, v = 4 : u * v = 4, u + v = 5 \Rightarrow

假检验

u = 2, v = 2 : u * v = 4, u + v = 4 \Rightarrow

假

u = - 1, v = - 4

分组为

(a x^{2} + ux) + (vx + c)

(2 x^{2} - x) + (- 4 x + 2)

= (2 x^{2} - x) + (- 4 x + 2)

从

2 x^{2} - x

分解出因式

x

:

x (2 x - 1)

2 x^{2} - x

使用指数法则:

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

x^{2} = xx

= 2 xx - x

因式分解出通项

x

= x (2 x - 1)

从

- 4 x + 2

分解出因式

- 2

:

- 2 (2 x - 1)

- 4 x + 2

将

4

改写为

2 \cdot 2

= - 2 \cdot 2 x + 2

因式分解出通项

- 2

= - 2 (2 x - 1)

= x (2 x - 1) - 2 (2 x - 1)

因式分解出通项

2 x - 1

= (2 x - 1) (x - 2)

= x (2 x - 1) (x - 2)

x (2 x - 1) (x - 2) = 0

使用零因数法则： If

ab = 0

then

a = 0

or

b = 0

x = 0 or 2 x - 1 = 0 or x - 2 = 0

解

2 x - 1 = 0 : x = \frac{1}{2}

2 x - 1 = 0

将

1

到右边

2 x - 1 = 0

两边加上

1

2 x - 1 + 1 = 0 + 1

化简

2 x = 1

2 x = 1

两边除以

2

2 x = 1

两边除以

2

\frac{2 x}{2} = \frac{1}{2}

化简

x = \frac{1}{2}

x = \frac{1}{2}

解

x - 2 = 0 : x = 2

x - 2 = 0

将

2

到右边

x - 2 = 0

两边加上

2

x - 2 + 2 = 0 + 2

化简

x = 2

x = 2

解为

x = 0, x = \frac{1}{2}, x = 2

x = 0, x = \frac{1}{2}, x = 2

验证解:

x = 0

真

, x = \frac{1}{2}

真

, x = 2

假

将它们代入

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

检验解是否符合

去除与方程不符的解。

代入

x = 0 :

真

1 - 0^{2} 1 - (1 - 0)^{2} - 0 \cdot (1 - 0) = 0

1 - 0^{2} 1 - (1 - 0)^{2} - 0 \cdot (1 - 0) = 0

1 - 0^{2} 1 - (1 - 0)^{2} - 0 \cdot (1 - 0)

使用法则

0^{a} = 0

0^{2} = 0

= 1 - 0 - (1 - 0)^{2} + 1 - 0 \cdot (1 - 0)

1 - 0 1 - (1 - 0)^{2} = 0

1 - 0 1 - (1 - 0)^{2}

1 - 0 = 1

1 - 0

数字相减:

1 - 0 = 1

= 1

使用法则

1 = 1

= 1

= 1 \cdot - (1 - 0)^{2} + 1

1 - (1 - 0)^{2} = 0

1 - (1 - 0)^{2}

(1 - 0)^{2} = 1

(1 - 0)^{2}

数字相减:

1 - 0 = 1

= 1^{2}

使用法则

1^{a} = 1

= 1

= 1 - 1

数字相减:

1 - 1 = 0

= 0

使用法则

0 = 0

= 0

= 1 \cdot 0

使用法则

0 \cdot a = 0

= 0

0 \cdot (1 - 0) = 0

0 \cdot (1 - 0)

数字相减:

1 - 0 = 1

= 0 \cdot 1

使用法则

0 \cdot a = 0

= 0

= 0 - 0

数字相减:

0 - 0 = 0

= 0

0 = 0

真

代入

x = \frac{1}{2} :

真

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

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

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

去除括号:

(a) = a

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

1 - (\frac{1}{2})^{2} 1 - (1 - \frac{1}{2})^{2} = \frac{3}{4}

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

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

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

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

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

使用指数法则:

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

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

使用法则

1^{a} = 1

1^{2} = 1

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

2^{2} = 4

= \frac{1}{4}

= 1 - \frac{1}{4}

化简

1 - \frac{1}{4} : \frac{3}{4}

1 - \frac{1}{4}

将项转换为分式:

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

= \frac{1 \cdot 4}{4} - \frac{1}{4}

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 4 - 1}{4}

1 \cdot 4 - 1 = 3

1 \cdot 4 - 1

数字相乘:

1 \cdot 4 = 4

= 4 - 1

数字相减:

4 - 1 = 3

= 3

= \frac{3}{4}

= \frac{3}{4}

使用根式运算法则:

n \frac{a}{b} = \frac{n a}{n b},

假定

a \geq 0, b \geq 0

= \frac{3}{4}

4 = 2

4

因式分解数字:

4 = 2^{2}

= 2^{2}

使用根式运算法则:

n a^{n} = a

2^{2} = 2

= 2

= \frac{3}{2}

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

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

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

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

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

化简

1 - \frac{1}{2} : \frac{1}{2}

1 - \frac{1}{2}

将项转换为分式:

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

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

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 2 - 1}{2}

1 \cdot 2 - 1 = 1

1 \cdot 2 - 1

数字相乘:

1 \cdot 2 = 2

= 2 - 1

数字相减:

2 - 1 = 1

= 1

= \frac{1}{2}

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

使用指数法则:

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

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

使用法则

1^{a} = 1

1^{2} = 1

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

2^{2} = 4

= \frac{1}{4}

= 1 - \frac{1}{4}

化简

1 - \frac{1}{4} : \frac{3}{4}

1 - \frac{1}{4}

将项转换为分式:

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

= \frac{1 \cdot 4}{4} - \frac{1}{4}

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 4 - 1}{4}

1 \cdot 4 - 1 = 3

1 \cdot 4 - 1

数字相乘:

1 \cdot 4 = 4

= 4 - 1

数字相减:

4 - 1 = 3

= 3

= \frac{3}{4}

= \frac{3}{4}

使用根式运算法则:

n \frac{a}{b} = \frac{n a}{n b},

假定

a \geq 0, b \geq 0

= \frac{3}{4}

4 = 2

4

因式分解数字:

4 = 2^{2}

= 2^{2}

使用根式运算法则:

n a^{n} = a

2^{2} = 2

= 2

= \frac{3}{2}

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

分式相乘:

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

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

33 = 3

33

使用根式运算法则:

a a = a

33 = 3

= 3

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

数字相乘:

2 \cdot 2 = 4

= \frac{3}{4}

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

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

化简

1 - \frac{1}{2} : \frac{1}{2}

1 - \frac{1}{2}

将项转换为分式:

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

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

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 2 - 1}{2}

1 \cdot 2 - 1 = 1

1 \cdot 2 - 1

数字相乘:

1 \cdot 2 = 2

= 2 - 1

数字相减:

2 - 1 = 1

= 1

= \frac{1}{2}

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

分式相乘:

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

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

数字相乘:

1 \cdot 1 = 1

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

数字相乘:

2 \cdot 2 = 4

= \frac{1}{4}

= \frac{3}{4} - \frac{1}{4}

使用法则

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

= \frac{3 - 1}{4}

数字相减:

3 - 1 = 2

= \frac{2}{4}

约分:

2

= \frac{1}{2}

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

真

代入

x = 2 :

假

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

化简

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

未定义

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

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

未定义

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

1 - 2^{2} = - 3

1 - 2^{2}

2^{2} = 4

= 1 - 4

数字相减:

1 - 4 = - 3

= - 3

= - 3 - (1 - 2)^{2} + 1

1 - (1 - 2)^{2} = 0

1 - (1 - 2)^{2}

(1 - 2)^{2} = 1

(1 - 2)^{2}

数字相减:

1 - 2 = - 1

= (- 1)^{2}

使用指数法则:

(- a)^{n} = a^{n},

若

n

是偶数

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

= 1^{2}

使用法则

1^{a} = 1

= 1

= 1 - 1

数字相减:

1 - 1 = 0

= 0

使用法则

0 = 0

= 0

= 0 \cdot - 3

a, a < 0

不在定义域

= 未定义

= 未定义

未定义

= 2

假

解为

x = 0, x = \frac{1}{2}

x = 0, x = \frac{1}{2}

将解代入原方程进行验证

将它们代入

arcsin (x) + arcsin (1 - x) = arccos (x)

检验解是否符合

去除与方程不符的解。

检验

0

的解:

真

0

代入

n = 1

0

对于

arcsin (x) + arcsin (1 - x) = arccos (x)

代入

x = 0

arcsin (0) + arcsin (1 - 0) = arccos (0)

整理后得

1.57079 \dots = 1.57079 \dots

\Rightarrow 真

检验

\frac{1}{2}

的解:

真

\frac{1}{2}

代入

n = 1

\frac{1}{2}

对于

arcsin (x) + arcsin (1 - x) = arccos (x)

代入

x = \frac{1}{2}

arcsin (\frac{1}{2}) + arcsin (1 - \frac{1}{2}) = arccos (\frac{1}{2})

整理后得

1.04719 \dots = 1.04719 \dots

\Rightarrow 真

x = 0, x = \frac{1}{2}

作图

流行的例子

3cos^2(x)+1=4sin(x)

3 cos^{2} (x) + 1 = 4 sin (x)

[2sin(4x)-1]*[1+tan(x)]=0

[2 sin (4 x) - 1] \cdot [1 + tan (x)] = 0

cos^2(x)=2cos(x)

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

sin(4θ)=(sqrt(3))/2

sin (4 θ) = \frac{3}{2}

2sin(θ)=-0.684

2 sin (θ) = - 0.684