zs

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

受欢迎的三角函数 >

(1+cot(p))tan(p)=3

解答

(1 + cot (p)) tan (p) = 3

解答

p = 1.10714 \dots + πn

+1

度数

p = 63.43494 \dots^{\circ} + 18 0^{\circ} n

求解步骤

(1 + cot (p)) tan (p) = 3

两边减去

3

tan (p) (1 + cot (p)) - 3 = 0

使用三角恒等式改写

- 3 + (1 + cot (p)) tan (p)

使用基本三角恒等式:

tan (x) = \frac{1}{cot ( x )}

= - 3 + (1 + cot (p)) \frac{1}{cot ( p )}

(1 + cot (p)) \frac{1}{cot ( p )} = \frac{1 + cot ( p )}{cot ( p )}

(1 + cot (p)) \frac{1}{cot ( p )}

分式相乘:

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

= \frac{1 \cdot ( 1 + cot ( p ) )}{cot ( p )}

1 \cdot (1 + cot (p)) = 1 + cot (p)

1 \cdot (1 + cot (p))

乘以:

1 \cdot (1 + cot (p)) = (1 + cot (p))

= (1 + cot (p))

去除括号:

(a) = a

= 1 + cot (p)

= \frac{1 + cot ( p )}{cot ( p )}

= - 3 + \frac{1 + cot ( p )}{cot ( p )}

- 3 + \frac{1 + cot ( p )}{cot ( p )} = 0

用替代法求解

- 3 + \frac{1 + cot ( p )}{cot ( p )} = 0

令

: cot (p) = u

- 3 + \frac{1 + u}{u} = 0

- 3 + \frac{1 + u}{u} = 0 : u = \frac{1}{2}

- 3 + \frac{1 + u}{u} = 0

在两边乘以

u

- 3 + \frac{1 + u}{u} = 0

在两边乘以

u

- 3 u + \frac{1 + u}{u} u = 0 \cdot u

化简

- 3 u + \frac{1 + u}{u} u = 0 \cdot u

化简

\frac{1 + u}{u} u : 1 + u

\frac{1 + u}{u} u

分式相乘:

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

= \frac{( 1 + u ) u}{u}

约分:

u

= 1 + u

化简

0 \cdot u : 0

0 \cdot u

使用法则

0 \cdot a = 0

= 0

- 3 u + 1 + u = 0

化简

- 3 u + 1 + u : - 2 u + 1

- 3 u + 1 + u

对同类项分组

= - 3 u + u + 1

同类项相加:

- 3 u + u = - 2 u

= - 2 u + 1

- 2 u + 1 = 0

- 2 u + 1 = 0

- 2 u + 1 = 0

将

1

到右边

- 2 u + 1 = 0

两边减去

1

- 2 u + 1 - 1 = 0 - 1

化简

- 2 u = - 1

- 2 u = - 1

两边除以

- 2

- 2 u = - 1

两边除以

- 2

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

化简

u = \frac{1}{2}

u = \frac{1}{2}

验证解

找到无定义的点（奇点）:

u = 0

取

- 3 + \frac{1 + u}{u}

的分母，令其等于零

u = 0

以下点无定义

u = 0

将不在定义域的点与解相综合:

u = \frac{1}{2}

u = cot (p)

代回

cot (p) = \frac{1}{2}

cot (p) = \frac{1}{2}

cot (p) = \frac{1}{2} : p = arccot (\frac{1}{2}) + πn

cot (p) = \frac{1}{2}

使用反三角函数性质

cot (p) = \frac{1}{2}

cot (p) = \frac{1}{2}

的通解

cot (x) = a \Rightarrow x = arccot (a) + πn

p = arccot (\frac{1}{2}) + πn

p = arccot (\frac{1}{2}) + πn

合并所有解

p = arccot (\frac{1}{2}) + πn

以小数形式表示解

p = 1.10714 \dots + πn

作图

流行的例子

csc(x)=sqrt(10)

31.21=40sin(25g)

tan(t)= 7/24 ,0<t< pi/2