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受欢迎的三角函数 >

(tan(x^2+6)-1)/(tan(x))=0

解答

\frac{tan ( x ^{2} + 6 ) - 1}{tan ( x )} = 0

解答

x \in R 无解

求解步骤

\frac{tan ( x ^{2} + 6 ) - 1}{tan ( x )} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

tan (x^{2} + 6) - 1 = 0

将

1

到右边

tan (x^{2} + 6) - 1 = 0

两边加上

1

tan (x^{2} + 6) - 1 + 1 = 0 + 1

化简

tan (x^{2} + 6) = 1

tan (x^{2} + 6) = 1

tan (x^{2} + 6) = 1

的通解

tan (x)

周期表（周期为

πn

）：

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

x^{2} + 6 = \frac{π}{4} + πn

x^{2} + 6 = \frac{π}{4} + πn

解

x^{2} + 6 = \frac{π}{4} + πn : x = \frac{π + 4 πn - 24}{2}, x = - \frac{π + 4 πn - 24}{2}

x^{2} + 6 = \frac{π}{4} + πn

将

6

到右边

x^{2} + 6 = \frac{π}{4} + πn

两边减去

6

x^{2} + 6 - 6 = \frac{π}{4} + πn - 6

化简

x^{2} = \frac{π}{4} + πn - 6

x^{2} = \frac{π}{4} + πn - 6

对于

x^{2} = f (a)

解为

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

x = \frac{π}{4} + πn - 6, x = - \frac{π}{4} + πn - 6

化简

\frac{π}{4} + πn - 6 : \frac{π + 4 πn - 24}{2}

\frac{π}{4} + πn - 6

化简

\frac{π}{4} + πn - 6 : \frac{π + 4 πn - 24}{4}

\frac{π}{4} + πn - 6

将项转换为分式:

πn = \frac{πn 4}{4}, 6 = \frac{6 \cdot 4}{4}

= \frac{π}{4} + \frac{πn \cdot 4}{4} - \frac{6 \cdot 4}{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{π + πn \cdot 4 - 6 \cdot 4}{4}

数字相乘:

6 \cdot 4 = 24

= \frac{π + 4 πn - 24}{4}

= \frac{π + πn \cdot 4 - 24}{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{π + 4 πn - 24}{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{π + 4 πn - 24}{2}

化简

- \frac{π}{4} + πn - 6 : - \frac{π + 4 πn - 24}{2}

- \frac{π}{4} + πn - 6

化简

\frac{π}{4} + πn - 6 : \frac{π + 4 πn - 24}{4}

\frac{π}{4} + πn - 6

将项转换为分式:

πn = \frac{πn 4}{4}, 6 = \frac{6 \cdot 4}{4}

= \frac{π}{4} + \frac{πn \cdot 4}{4} - \frac{6 \cdot 4}{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{π + πn \cdot 4 - 6 \cdot 4}{4}

数字相乘:

6 \cdot 4 = 24

= \frac{π + 4 πn - 24}{4}

= - \frac{π + 4 πn - 24}{4}

化简

\frac{π + πn \cdot 4 - 24}{4} : \frac{π + 4 πn - 24}{2}

\frac{π + πn \cdot 4 - 24}{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{π + 4 πn - 24}{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{π + 4 πn - 24}{2}

= - \frac{π + 4 πn - 24}{2}

x = \frac{π + 4 πn - 24}{2}, x = - \frac{π + 4 πn - 24}{2}

x = \frac{π + 4 πn - 24}{2}, x = - \frac{π + 4 πn - 24}{2}

因为方程对以下值无定义:

\frac{π + 4 πn - 24}{2}, - \frac{π + 4 πn - 24}{2}

x \in R 无解

作图

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