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受欢迎的三角函数 >

4cos^2(x)+1=0

解答

4 cos^{2} (x) + 1 = 0

解答

x \in R 无解

求解步骤

4 cos^{2} (x) + 1 = 0

用替代法求解

4 cos^{2} (x) + 1 = 0

令

: cos (x) = u

4 u^{2} + 1 = 0

4 u^{2} + 1 = 0 : u = i \frac{1}{2}, u = - i \frac{1}{2}

4 u^{2} + 1 = 0

将

1

到右边

4 u^{2} + 1 = 0

两边减去

1

4 u^{2} + 1 - 1 = 0 - 1

化简

4 u^{2} = - 1

4 u^{2} = - 1

两边除以

4

4 u^{2} = - 1

两边除以

4

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

化简

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

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

对于

x^{2} = f (a)

解为

x = f (a), - f (a)

u = - \frac{1}{4}, u = - - \frac{1}{4}

化简

- \frac{1}{4} : i \frac{1}{2}

- \frac{1}{4}

使用根式运算法则:

- a = - 1 a

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

= - 1 \frac{1}{4}

使用虚数运算法则:

- 1 = i

= i \frac{1}{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{1}{4} = \frac{1}{4}

= i \frac{1}{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

= i \frac{1}{2}

使用法则

1 = 1

= i \frac{1}{2}

将

i \frac{1}{2}

改写成标准复数形式:

\frac{1}{2} i

i \frac{1}{2}

分式相乘:

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

= \frac{1 i}{2}

乘以:

1 i = i

= \frac{i}{2}

= \frac{1}{2} i

化简

- - \frac{1}{4} : - i \frac{1}{2}

- - \frac{1}{4}

化简

- \frac{1}{4} : i \frac{1}{2}

- \frac{1}{4}

使用根式运算法则:

- a = - 1 a

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

= - 1 \frac{1}{4}

使用虚数运算法则:

- 1 = i

= i \frac{1}{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{1}{4} = \frac{1}{4}

= i \frac{1}{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

= i \frac{1}{2}

= - i \frac{1}{2}

使用法则

1 = 1

= - \frac{1}{2} i

u = i \frac{1}{2}, u = - i \frac{1}{2}

u = cos (x)

代回

cos (x) = i \frac{1}{2}, cos (x) = - i \frac{1}{2}

cos (x) = i \frac{1}{2}, cos (x) = - i \frac{1}{2}

cos (x) = i \frac{1}{2} :

无解

cos (x) = i \frac{1}{2}

无解

cos (x) = - i \frac{1}{2} :

无解

cos (x) = - i \frac{1}{2}

无解

合并所有解

x \in R 无解

作图

流行的例子

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