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人気のある三角関数 >

(csc(x))/(cot(x))=csc(x)sec(x)

解

\frac{csc ( x )}{cot ( x )} = csc (x) sec (x)

解

以下の解はない : x \in R

解答ステップ

\frac{csc ( x )}{cot ( x )} = csc (x) sec (x)

両辺から

csc (x) sec (x)

を引く

\frac{csc ( x )}{cot ( x )} - csc (x) sec (x) = 0

簡素化

\frac{csc ( x )}{cot ( x )} - csc (x) sec (x) : \frac{csc ( x ) - csc ( x ) sec ( x ) cot ( x )}{cot ( x )}

\frac{csc ( x )}{cot ( x )} - csc (x) sec (x)

元を分数に変換する:

csc (x) sec (x) = \frac{csc ( x ) sec ( x ) cot ( x )}{cot ( x )}

= \frac{csc ( x )}{cot ( x )} - \frac{csc ( x ) sec ( x ) cot ( x )}{cot ( x )}

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{csc ( x ) - csc ( x ) sec ( x ) cot ( x )}{cot ( x )}

\frac{csc ( x ) - csc ( x ) sec ( x ) cot ( x )}{cot ( x )} = 0

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

csc (x) - csc (x) sec (x) cot (x) = 0

因数

csc (x) - csc (x) sec (x) cot (x) : csc (x) (1 - sec (x) cot (x))

csc (x) - csc (x) sec (x) cot (x)

共通項をくくり出す

csc (x)

= csc (x) (1 - sec (x) cot (x))

csc (x) (1 - sec (x) cot (x)) = 0

各部分を別個に解く

csc (x) = 0 or 1 - sec (x) cot (x) = 0

csc (x) = 0 :

解なし

csc (x) = 0

csc (x) \leq - 1 or csc (x) \geq 1

解なし

1 - sec (x) cot (x) = 0 :

解なし

1 - sec (x) cot (x) = 0

サイン, コサインで表わす

1 - cot (x) sec (x)

基本的な三角関数の公式を使用する:

cot (x) = \frac{cos ( x )}{sin ( x )}

= 1 - \frac{cos ( x )}{sin ( x )} sec (x)

基本的な三角関数の公式を使用する:

sec (x) = \frac{1}{cos ( x )}

= 1 - \frac{cos ( x )}{sin ( x )} \cdot \frac{1}{cos ( x )}

簡素化

1 - \frac{cos ( x )}{sin ( x )} \cdot \frac{1}{cos ( x )} : \frac{sin ( x ) - 1}{sin ( x )}

1 - \frac{cos ( x )}{sin ( x )} \cdot \frac{1}{cos ( x )}

\frac{cos ( x )}{sin ( x )} \cdot \frac{1}{cos ( x )} = \frac{1}{sin ( x )}

\frac{cos ( x )}{sin ( x )} \cdot \frac{1}{cos ( x )}

分数を乗じる:

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

= \frac{cos ( x ) \cdot 1}{sin ( x ) cos ( x )}

共通因数を約分する:

cos (x)

= \frac{1}{sin ( x )}

= 1 - \frac{1}{sin ( x )}

元を分数に変換する:

1 = \frac{1 sin ( x )}{sin ( x )}

= \frac{1 \cdot sin ( x )}{sin ( x )} - \frac{1}{sin ( x )}

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 \cdot sin ( x ) - 1}{sin ( x )}

乗算:

1 \cdot sin (x) = sin (x)

= \frac{sin ( x ) - 1}{sin ( x )}

= \frac{sin ( x ) - 1}{sin ( x )}

\frac{- 1 + sin ( x )}{sin ( x )} = 0

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

- 1 + sin (x) = 0

1

を右側に移動します

- 1 + sin (x) = 0

両辺に

1

を足す

- 1 + sin (x) + 1 = 0 + 1

簡素化

sin (x) = 1

sin (x) = 1

以下の一般解

sin (x) = 1

sin (x)

2 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} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

x = \frac{π}{2} + 2 πn

x = \frac{π}{2} + 2 πn

equationは以下で未定義のため:

\frac{π}{2} + 2 πn

解なし

すべての解を組み合わせる

以下の解はない : x \in R

グラフ

人気の例

sin(θ)= 1/(sqrt(3))

sin (θ) = \frac{1}{3}

cos (θ) = 0.9

4 - 4 sin (θ) = 4

4cos(x)sin(x)=-5sin(x)

4 cos (x) sin (x) = - 5 sin (x)

2sin(x)+cot(x)-csc(x)=0

2 sin (x) + cot (x) - csc (x) = 0