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人気のある >

1/((1+tan^2(o)+1))+1/((1+cot^2(o)))=1

解

\frac{1}{( 1 + tan ^{2} ( o ) + 1 )} + \frac{1}{( 1 + cot ^{2} ( o ) )} = 1

解

以下の解はない : o \in R

解答ステップ

\frac{1}{( 1 + tan ^{2} ( o ) + 1 )} + \frac{1}{( 1 + cot ^{2} ( o ) )} = 1

両辺から

1

を引く

\frac{cot ^{2} ( o ) + tan ^{2} ( o ) + 3}{( tan ^{2} ( o ) + 2 ) ( cot ^{2} ( o ) + 1 )} - 1 = 0

簡素化

\frac{cot ^{2} ( o ) + tan ^{2} ( o ) + 3}{( tan ^{2} ( o ) + 2 ) ( cot ^{2} ( o ) + 1 )} - 1 : \frac{- cot ^{2} ( o ) - tan ^{2} ( o ) cot ^{2} ( o ) + 1}{( tan ^{2} ( o ) + 2 ) ( cot ^{2} ( o ) + 1 )}

\frac{cot ^{2} ( o ) + tan ^{2} ( o ) + 3}{( tan ^{2} ( o ) + 2 ) ( cot ^{2} ( o ) + 1 )} - 1

元を分数に変換する:

1 = \frac{1 ( tan ^{2} ( o ) + 2 ) ( cot ^{2} ( o ) + 1 )}{( tan ^{2} ( o ) + 2 ) ( cot ^{2} ( o ) + 1 )}

= \frac{cot ^{2} ( o ) + tan ^{2} ( o ) + 3}{( tan ^{2} ( o ) + 2 ) ( cot ^{2} ( o ) + 1 )} - \frac{1 \cdot ( tan ^{2} ( o ) + 2 ) ( cot ^{2} ( o ) + 1 )}{( tan ^{2} ( o ) + 2 ) ( cot ^{2} ( o ) + 1 )}

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{cot ^{2} ( o ) + tan ^{2} ( o ) + 3 - 1 \cdot ( tan ^{2} ( o ) + 2 ) ( cot ^{2} ( o ) + 1 )}{( tan ^{2} ( o ) + 2 ) ( cot ^{2} ( o ) + 1 )}

乗算:

1 \cdot (tan^{2} (o) + 2) = (tan^{2} (o) + 2)

= \frac{cot ^{2} ( o ) + tan ^{2} ( o ) + 3 - ( tan ^{2} ( o ) + 2 ) ( cot ^{2} ( o ) + 1 )}{( tan ^{2} ( o ) + 2 ) ( cot ^{2} ( o ) + 1 )}

拡張

cot^{2} (o) + tan^{2} (o) + 3 - (tan^{2} (o) + 2) (cot^{2} (o) + 1) : - cot^{2} (o) - tan^{2} (o) cot^{2} (o) + 1

cot^{2} (o) + tan^{2} (o) + 3 - (tan^{2} (o) + 2) (cot^{2} (o) + 1)

拡張

- (tan^{2} (o) + 2) (cot^{2} (o) + 1) : - tan^{2} (o) cot^{2} (o) - tan^{2} (o) - 2 cot^{2} (o) - 2

拡張

(tan^{2} (o) + 2) (cot^{2} (o) + 1) : tan^{2} (o) cot^{2} (o) + tan^{2} (o) + 2 cot^{2} (o) + 2

(tan^{2} (o) + 2) (cot^{2} (o) + 1)

FOIL メソッドを適用する:

(a + b) (c + d) = a c + a d + b c + b d

a = tan^{2} (o), b = 2, c = cot^{2} (o), d = 1

= tan^{2} (o) cot^{2} (o) + tan^{2} (o) \cdot 1 + 2 cot^{2} (o) + 2 \cdot 1

= tan^{2} (o) cot^{2} (o) + 1 \cdot tan^{2} (o) + 2 cot^{2} (o) + 2 \cdot 1

簡素化

tan^{2} (o) cot^{2} (o) + 1 \cdot tan^{2} (o) + 2 cot^{2} (o) + 2 \cdot 1 : tan^{2} (o) cot^{2} (o) + tan^{2} (o) + 2 cot^{2} (o) + 2

tan^{2} (o) cot^{2} (o) + 1 \cdot tan^{2} (o) + 2 cot^{2} (o) + 2 \cdot 1

乗算:

1 \cdot tan^{2} (o) = tan^{2} (o)

= tan^{2} (o) cot^{2} (o) + tan^{2} (o) + 2 cot^{2} (o) + 2 \cdot 1

数を乗じる:

2 \cdot 1 = 2

= tan^{2} (o) cot^{2} (o) + tan^{2} (o) + 2 cot^{2} (o) + 2

= tan^{2} (o) cot^{2} (o) + tan^{2} (o) + 2 cot^{2} (o) + 2

= - (tan^{2} (o) cot^{2} (o) + tan^{2} (o) + 2 cot^{2} (o) + 2)

括弧を分配する

= - (tan^{2} (o) cot^{2} (o)) - (tan^{2} (o)) - (2 cot^{2} (o)) - (2)

マイナス・プラスの規則を適用する

+ (- a) = - a

= - tan^{2} (o) cot^{2} (o) - tan^{2} (o) - 2 cot^{2} (o) - 2

= cot^{2} (o) + tan^{2} (o) + 3 - tan^{2} (o) cot^{2} (o) - tan^{2} (o) - 2 cot^{2} (o) - 2

簡素化

cot^{2} (o) + tan^{2} (o) + 3 - tan^{2} (o) cot^{2} (o) - tan^{2} (o) - 2 cot^{2} (o) - 2 : - cot^{2} (o) - tan^{2} (o) cot^{2} (o) + 1

cot^{2} (o) + tan^{2} (o) + 3 - tan^{2} (o) cot^{2} (o) - tan^{2} (o) - 2 cot^{2} (o) - 2

条件のようなグループ

= cot^{2} (o) + tan^{2} (o) - tan^{2} (o) cot^{2} (o) - tan^{2} (o) - 2 cot^{2} (o) + 3 - 2

類似した元を足す:

cot^{2} (o) - 2 cot^{2} (o) = - cot^{2} (o)

= - cot^{2} (o) + tan^{2} (o) - tan^{2} (o) cot^{2} (o) - tan^{2} (o) + 3 - 2

類似した元を足す:

tan^{2} (o) - tan^{2} (o) = 0

= - cot^{2} (o) - tan^{2} (o) cot^{2} (o) + 3 - 2

数を足す/引く:

3 - 2 = 1

= - cot^{2} (o) - tan^{2} (o) cot^{2} (o) + 1

= - cot^{2} (o) - tan^{2} (o) cot^{2} (o) + 1

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

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

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

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

三角関数の公式を使用して書き換える

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

基本的な三角関数の公式を使用する:

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

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

簡素化

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

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

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

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

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

(\frac{1}{cot ( o )})^{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} ( o )}

規則を適用

1^{a} = 1

1^{2} = 1

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

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

分数を乗じる:

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

= \frac{1 \cdot cot ^{2} ( o )}{cot ^{2} ( o )}

共通因数を約分する:

cot^{2} (o)

= 1

= 1 - cot^{2} (o) - 1

条件のようなグループ

= - cot^{2} (o) + 1 - 1

1 - 1 = 0

= - cot^{2} (o)

= - cot^{2} (o)

- cot^{2} (o) = 0

以下で両辺を割る

- 1

- cot^{2} (o) = 0

以下で両辺を割る

- 1

- cot^{2} (o) = 0

以下で両辺を割る

- 1

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

簡素化

cot^{2} (o) = 0

cot^{2} (o) = 0

規則を適用

x^{n} = 0 \Rightarrow x = 0

cot (o) = 0

以下の一般解

cot (o) = 0

cot (x)

πn

循環を含む周期性テーブル:

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} cot (x) \mp \infty 31 \frac{3}{3} 0 - \frac{3}{3} - 1 - 3

o = \frac{π}{2} + πn

o = \frac{π}{2} + πn

equationは以下で未定義のため:

\frac{π}{2} + πn

以下の解はない : o \in R

グラフ

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solvefor t,0.08=0.1cos(4t)解く

t, 0.08 = 0.1 cos (4 t)