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受欢迎的三角函数 >

4=tan^2(45+x/2)

解答

4 = tan^{2} (4 5^{\circ} + \frac{x}{2})

解答

x = 2 \cdot 1.10714 \dots + 36 0^{\circ} n - 9 0^{\circ}, x = - 2 \cdot 1.10714 \dots + 36 0^{\circ} n - 9 0^{\circ}

+1

弧度

x = 2 \cdot 1.10714 \dots - \frac{π}{2} + 2 πn, x = - 2 \cdot 1.10714 \dots - \frac{π}{2} + 2 πn

求解步骤

4 = tan^{2} (4 5^{\circ} + \frac{x}{2})

交换两边

tan^{2} (4 5^{\circ} + \frac{x}{2}) = 4

用替代法求解

tan^{2} (4 5^{\circ} + \frac{x}{2}) = 4

令

: tan (4 5^{\circ} + \frac{x}{2}) = u

u^{2} = 4

u^{2} = 4 : u = 2, u = - 2

u^{2} = 4

对于

x^{2} = f (a)

解为

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

u = 4, u = - 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

- 4 = - 2

- 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

= - 2

u = 2, u = - 2

u = tan (4 5^{\circ} + \frac{x}{2})

代回

tan (4 5^{\circ} + \frac{x}{2}) = 2, tan (4 5^{\circ} + \frac{x}{2}) = - 2

tan (4 5^{\circ} + \frac{x}{2}) = 2, tan (4 5^{\circ} + \frac{x}{2}) = - 2

tan (4 5^{\circ} + \frac{x}{2}) = 2 : x = 2 arctan (2) + 36 0^{\circ} n - 9 0^{\circ}

tan (4 5^{\circ} + \frac{x}{2}) = 2

使用反三角函数性质

tan (4 5^{\circ} + \frac{x}{2}) = 2

tan (4 5^{\circ} + \frac{x}{2}) = 2

的通解

tan (x) = a \Rightarrow x = arctan (a) + 18 0^{\circ} n

4 5^{\circ} + \frac{x}{2} = arctan (2) + 18 0^{\circ} n

4 5^{\circ} + \frac{x}{2} = arctan (2) + 18 0^{\circ} n

解

4 5^{\circ} + \frac{x}{2} = arctan (2) + 18 0^{\circ} n : x = 2 arctan (2) + 36 0^{\circ} n - 9 0^{\circ}

4 5^{\circ} + \frac{x}{2} = arctan (2) + 18 0^{\circ} n

将

4 5^{\circ}

到右边

4 5^{\circ} + \frac{x}{2} = arctan (2) + 18 0^{\circ} n

两边减去

4 5^{\circ}

4 5^{\circ} + \frac{x}{2} - 4 5^{\circ} = arctan (2) + 18 0^{\circ} n - 4 5^{\circ}

化简

\frac{x}{2} = arctan (2) + 18 0^{\circ} n - 4 5^{\circ}

\frac{x}{2} = arctan (2) + 18 0^{\circ} n - 4 5^{\circ}

在两边乘以

2

\frac{x}{2} = arctan (2) + 18 0^{\circ} n - 4 5^{\circ}

在两边乘以

2

\frac{2 x}{2} = 2 arctan (2) + 36 0^{\circ} n - 2 \cdot 4 5^{\circ}

化简

\frac{2 x}{2} = 2 arctan (2) + 36 0^{\circ} n - 2 \cdot 4 5^{\circ}

化简

\frac{2 x}{2} : x

\frac{2 x}{2}

数字相除:

\frac{2}{2} = 1

= x

化简

2 arctan (2) + 36 0^{\circ} n - 2 \cdot 4 5^{\circ} : 2 arctan (2) + 36 0^{\circ} n - 9 0^{\circ}

2 arctan (2) + 36 0^{\circ} n - 2 \cdot 4 5^{\circ}

2 \cdot 4 5^{\circ} = 9 0^{\circ}

2 \cdot 4 5^{\circ}

分式相乘:

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

= 9 0^{\circ}

约分:

2

= 9 0^{\circ}

= 2 arctan (2) + 36 0^{\circ} n - 9 0^{\circ}

x = 2 arctan (2) + 36 0^{\circ} n - 9 0^{\circ}

x = 2 arctan (2) + 36 0^{\circ} n - 9 0^{\circ}

x = 2 arctan (2) + 36 0^{\circ} n - 9 0^{\circ}

x = 2 arctan (2) + 36 0^{\circ} n - 9 0^{\circ}

tan (4 5^{\circ} + \frac{x}{2}) = - 2 : x = - 2 arctan (2) + 36 0^{\circ} n - 9 0^{\circ}

tan (4 5^{\circ} + \frac{x}{2}) = - 2

使用反三角函数性质

tan (4 5^{\circ} + \frac{x}{2}) = - 2

tan (4 5^{\circ} + \frac{x}{2}) = - 2

的通解

tan (x) = - a \Rightarrow x = arctan (- a) + 18 0^{\circ} n

4 5^{\circ} + \frac{x}{2} = arctan (- 2) + 18 0^{\circ} n

4 5^{\circ} + \frac{x}{2} = arctan (- 2) + 18 0^{\circ} n

解

4 5^{\circ} + \frac{x}{2} = arctan (- 2) + 18 0^{\circ} n : x = - 2 arctan (2) + 36 0^{\circ} n - 9 0^{\circ}

4 5^{\circ} + \frac{x}{2} = arctan (- 2) + 18 0^{\circ} n

化简

arctan (- 2) + 18 0^{\circ} n : - arctan (2) + 18 0^{\circ} n

arctan (- 2) + 18 0^{\circ} n

利用以下特性:

arctan (- x) = - arctan (x)

arctan (- 2) = - arctan (2)

= - arctan (2) + 18 0^{\circ} n

4 5^{\circ} + \frac{x}{2} = - arctan (2) + 18 0^{\circ} n

将

4 5^{\circ}

到右边

4 5^{\circ} + \frac{x}{2} = - arctan (2) + 18 0^{\circ} n

两边减去

4 5^{\circ}

4 5^{\circ} + \frac{x}{2} - 4 5^{\circ} = - arctan (2) + 18 0^{\circ} n - 4 5^{\circ}

化简

\frac{x}{2} = - arctan (2) + 18 0^{\circ} n - 4 5^{\circ}

\frac{x}{2} = - arctan (2) + 18 0^{\circ} n - 4 5^{\circ}

在两边乘以

2

\frac{x}{2} = - arctan (2) + 18 0^{\circ} n - 4 5^{\circ}

在两边乘以

2

\frac{2 x}{2} = - 2 arctan (2) + 36 0^{\circ} n - 2 \cdot 4 5^{\circ}

化简

\frac{2 x}{2} = - 2 arctan (2) + 36 0^{\circ} n - 2 \cdot 4 5^{\circ}

化简

\frac{2 x}{2} : x

\frac{2 x}{2}

数字相除:

\frac{2}{2} = 1

= x

化简

- 2 arctan (2) + 36 0^{\circ} n - 2 \cdot 4 5^{\circ} : - 2 arctan (2) + 36 0^{\circ} n - 9 0^{\circ}

- 2 arctan (2) + 36 0^{\circ} n - 2 \cdot 4 5^{\circ}

2 \cdot 4 5^{\circ} = 9 0^{\circ}

2 \cdot 4 5^{\circ}

分式相乘:

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

= 9 0^{\circ}

约分:

2

= 9 0^{\circ}

= - 2 arctan (2) + 36 0^{\circ} n - 9 0^{\circ}

x = - 2 arctan (2) + 36 0^{\circ} n - 9 0^{\circ}

x = - 2 arctan (2) + 36 0^{\circ} n - 9 0^{\circ}

x = - 2 arctan (2) + 36 0^{\circ} n - 9 0^{\circ}

x = - 2 arctan (2) + 36 0^{\circ} n - 9 0^{\circ}

合并所有解

x = 2 arctan (2) + 36 0^{\circ} n - 9 0^{\circ}, x = - 2 arctan (2) + 36 0^{\circ} n - 9 0^{\circ}

以小数形式表示解

x = 2 \cdot 1.10714 \dots + 36 0^{\circ} n - 9 0^{\circ}, x = - 2 \cdot 1.10714 \dots + 36 0^{\circ} n - 9 0^{\circ}

作图

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