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人気のある三角関数 >

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

解

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

解

以下の解はない : A \in R

解答ステップ

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

両辺から

cot (A)

を引く

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

簡素化

\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)

元を分数に変換する:

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 )}

分母が等しいので, 分数を組み合わせる:

\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

三角関数の公式を使用して書き換える

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

基本的な三角関数の公式を使用する:

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

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

簡素化

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}

指数の規則を適用する:

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

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

規則を適用

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 )}

分数を乗じる:

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

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

共通因数を約分する:

cot (A)

= 1 \cdot 2

数を乗じる:

1 \cdot 2 = 2

= 2

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

条件のようなグループ

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

数を足す/引く:

1 - 2 = - 1

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

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

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

置換で解く

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

仮定:

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

以下で両辺を乗じる:

u^{2}

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

以下で両辺を乗じる:

u^{2}

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

簡素化

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

簡素化

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

- 1 \cdot u^{2}

乗算:

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

= - u^{2}

簡素化

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

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

分数を乗じる:

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

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

共通因数を約分する:

u^{2}

= - 1

簡素化

0 \cdot u^{2} : 0

0 \cdot u^{2}

規則を適用

0 \cdot a = 0

= 0

- u^{2} - 1 = 0

- u^{2} - 1 = 0

- u^{2} - 1 = 0

解く

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

- u^{2} - 1 = 0

1

を右側に移動します

- u^{2} - 1 = 0

両辺に

1

を足す

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

簡素化

- u^{2} = 1

- u^{2} = 1

以下で両辺を割る

- 1

- u^{2} = 1

以下で両辺を割る

- 1

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

簡素化

u^{2} = - 1

u^{2} = - 1

x^{2} = f (a)

の場合, 解は

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

u = - 1, u = - - 1

簡素化

- 1 : i

- 1

虚数の規則を適用する:

- 1 = i

= i

簡素化

- - 1 : - i

- - 1

虚数の規則を適用する:

- 1 = i

= - i

u = i, u = - i

u = i, u = - i

代用を戻す

u = cot (A)

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

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

cot (A) = i :

解なし

cot (A) = i

解なし

cot (A) = - i :

解なし

cot (A) = - i

解なし

すべての解を組み合わせる

以下の解はない : A \in R

グラフ

人気の例

cos(4θ)=cos(2θ),180<= θ<= 360

cos (4 θ) = cos (2 θ), 18 0^{\circ} \leq θ \leq 36 0^{\circ}

sqrt(2)sin(x)=cos(x)

2 sin (x) = cos (x)

8cos(2x)=8-8cos(2x)

8 cos (2 x) = 8 - 8 cos (2 x)

-(2)cos(10t)=(6)sin(10t)

- (2) cos (10 t) = (6) sin (10 t)

cot (x) = \frac{1}{4}