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受欢迎的三角函数 >

cos^4(a)=3+4cos^2(a)+cos^4(a)

解答

cos^{4} (a) = 3 + 4 cos^{2} (a) + cos^{4} (a)

解答

a \in R 无解

求解步骤

cos^{4} (a) = 3 + 4 cos^{2} (a) + cos^{4} (a)

用替代法求解

cos^{4} (a) = 3 + 4 cos^{2} (a) + cos^{4} (a)

令

: cos (a) = u

u^{4} = 3 + 4 u^{2} + u^{4}

u^{4} = 3 + 4 u^{2} + u^{4} : u = i \frac{3}{2}, u = - i \frac{3}{2}

u^{4} = 3 + 4 u^{2} + u^{4}

交换两边

3 + 4 u^{2} + u^{4} = u^{4}

将

3

到右边

3 + 4 u^{2} + u^{4} = u^{4}

两边减去

3

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

化简

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

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

将

u^{4}

para o lado esquerdo

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

两边减去

u^{4}

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

化简

4 u^{2} = - 3

4 u^{2} = - 3

两边除以

4

4 u^{2} = - 3

两边除以

4

\frac{4 u ^{2}}{4} = \frac{- 3}{4}

化简

u^{2} = - \frac{3}{4}

u^{2} = - \frac{3}{4}

对于

x^{2} = f (a)

解为

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

u = - \frac{3}{4}, u = - - \frac{3}{4}

化简

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

- \frac{3}{4}

使用根式运算法则:

- a = - 1 a

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

= - 1 \frac{3}{4}

使用虚数运算法则:

- 1 = i

= i \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} = \frac{3}{4}

= i \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

= i \frac{3}{2}

将

i \frac{3}{2}

改写成标准复数形式:

\frac{3}{2} i

i \frac{3}{2}

分式相乘:

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

= \frac{3 i}{2}

= \frac{3}{2} i

化简

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

- - \frac{3}{4}

化简

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

- \frac{3}{4}

使用根式运算法则:

- a = - 1 a

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

= - 1 \frac{3}{4}

使用虚数运算法则:

- 1 = i

= i \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} = \frac{3}{4}

= i \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

= i \frac{3}{2}

= - \frac{3}{2} i

= - i \frac{3}{2}

u = i \frac{3}{2}, u = - i \frac{3}{2}

u = cos (a)

代回

cos (a) = i \frac{3}{2}, cos (a) = - i \frac{3}{2}

cos (a) = i \frac{3}{2}, cos (a) = - i \frac{3}{2}

cos (a) = i \frac{3}{2} :

无解

cos (a) = i \frac{3}{2}

无解

cos (a) = - i \frac{3}{2} :

无解

cos (a) = - i \frac{3}{2}

无解

合并所有解

a \in R 无解

作图

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