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受欢迎的三角函数 >

(1-tan^2(A))/(2tan(A))=cot(A)

解答

\frac{1 - tan ^{2} ( A )}{2 tan ( A )} = cot (A)

解答

A \in R 无解

求解步骤

\frac{1 - tan ^{2} ( A )}{2 tan ( A )} = cot (A)

两边减去

cot (A)

\frac{1 - tan ^{2} ( A )}{2 tan ( A )} - cot (A) = 0

化简

\frac{1 - tan ^{2} ( A )}{2 tan ( A )} - cot (A) : \frac{1 - tan ^{2} ( A ) - 2 cot ( A ) tan ( A )}{2 tan ( A )}

\frac{1 - tan ^{2} ( A )}{2 tan ( A )} - cot (A)

将项转换为分式:

cot (A) = \frac{cot ( A ) 2 tan ( A )}{2 tan ( A )}

= \frac{1 - tan ^{2} ( A )}{2 tan ( A )} - \frac{cot ( A ) \cdot 2 tan ( A )}{2 tan ( A )}

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{1 - tan ^{2} ( A ) - cot ( A ) \cdot 2 tan ( A )}{2 tan ( A )}

\frac{1 - tan ^{2} ( A ) - 2 cot ( A ) tan ( A )}{2 tan ( A )} = 0

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

1 - tan^{2} (A) - 2 cot (A) tan (A) = 0

使用三角恒等式改写

1 - tan^{2} (A) - 2 cot (A) tan (A)

使用基本三角恒等式:

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

= 1 - (\frac{1}{cot ( A )})^{2} - 2 cot (A) \frac{1}{cot ( A )}

化简

1 - (\frac{1}{cot ( A )})^{2} - 2 cot (A) \frac{1}{cot ( A )} : - \frac{1}{cot ^{2} ( A )} - 1

1 - (\frac{1}{cot ( A )})^{2} - 2 cot (A) \frac{1}{cot ( A )}

(\frac{1}{cot ( A )})^{2} = \frac{1}{cot ^{2} ( A )}

(\frac{1}{cot ( A )})^{2}

使用指数法则:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{1 ^{2}}{cot ^{2} ( A )}

使用法则

1^{a} = 1

1^{2} = 1

= \frac{1}{cot ^{2} ( A )}

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

2 cot (A) \frac{1}{cot ( A )}

分式相乘:

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

= \frac{1 \cdot 2 cot ( A )}{cot ( A )}

约分:

cot (A)

= 1 \cdot 2

数字相乘:

1 \cdot 2 = 2

= 2

= 1 - \frac{1}{cot ^{2} ( A )} - 2

对同类项分组

= - \frac{1}{cot ^{2} ( A )} + 1 - 2

数字相加/相减:

1 - 2 = - 1

= - \frac{1}{cot ^{2} ( A )} - 1

= - \frac{1}{cot ^{2} ( A )} - 1

- 1 - \frac{1}{cot ^{2} ( A )} = 0

用替代法求解

- 1 - \frac{1}{cot ^{2} ( A )} = 0

令

: cot (A) = u

- 1 - \frac{1}{u ^{2}} = 0

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

- 1 - \frac{1}{u ^{2}} = 0

在两边乘以

u^{2}

- 1 - \frac{1}{u ^{2}} = 0

在两边乘以

u^{2}

- 1 \cdot u^{2} - \frac{1}{u ^{2}} u^{2} = 0 \cdot u^{2}

化简

- 1 \cdot u^{2} - \frac{1}{u ^{2}} u^{2} = 0 \cdot u^{2}

化简

- 1 \cdot u^{2} : - u^{2}

- 1 \cdot u^{2}

乘以:

1 \cdot u^{2} = u^{2}

= - u^{2}

化简

- \frac{1}{u ^{2}} u^{2} : - 1

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

分式相乘:

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

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

约分:

u^{2}

= - 1

化简

0 \cdot u^{2} : 0

0 \cdot u^{2}

使用法则

0 \cdot a = 0

= 0

- u^{2} - 1 = 0

- u^{2} - 1 = 0

- u^{2} - 1 = 0

解

- u^{2} - 1 = 0 : u = i, u = - i

- u^{2} - 1 = 0

将

1

到右边

- u^{2} - 1 = 0

两边加上

1

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

化简

- u^{2} = 1

- u^{2} = 1

两边除以

- 1

- u^{2} = 1

两边除以

- 1

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

化简

u^{2} = - 1

u^{2} = - 1

对于

x^{2} = f (a)

解为

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

u = - 1, u = - - 1

化简

- 1 : i

- 1

使用虚数运算法则:

- 1 = i

= i

化简

- - 1 : - i

- - 1

使用虚数运算法则:

- 1 = i

= - i

u = i, u = - i

u = i, u = - i

u = cot (A)

代回

cot (A) = i, cot (A) = - i

cot (A) = i, cot (A) = - i

cot (A) = i :

无解

cot (A) = i

无解

cot (A) = - i :

无解

cot (A) = - i

无解

合并所有解

A \in R 无解

作图

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