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人気のある三角関数 >

cot(a)sec(a)=cos(a)

解

cot (a) sec (a) = cos (a)

解

以下の解はない : a \in R

解答ステップ

cot (a) sec (a) = cos (a)

両辺から

cos (a)

を引く

cot (a) sec (a) - cos (a) = 0

サイン, コサインで表わす

- cos (a) + cot (a) sec (a)

基本的な三角関数の公式を使用する:

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

= - cos (a) + \frac{cos ( a )}{sin ( a )} sec (a)

基本的な三角関数の公式を使用する:

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

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

簡素化

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

- cos (a) + \frac{cos ( a )}{sin ( a )} \cdot \frac{1}{cos ( a )}

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

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

分数を乗じる:

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

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

共通因数を約分する:

cos (a)

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

= - cos (a) + \frac{1}{sin ( a )}

元を分数に変換する:

cos (a) = \frac{cos ( a ) sin ( a )}{sin ( a )}

= - \frac{cos ( a ) sin ( a )}{sin ( a )} + \frac{1}{sin ( 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{- cos ( a ) sin ( a ) + 1}{sin ( a )}

= \frac{- cos ( a ) sin ( a ) + 1}{sin ( a )}

\frac{1 - cos ( a ) sin ( a )}{sin ( a )} = 0

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

1 - cos (a) sin (a) = 0

三角関数の公式を使用して書き換える

1 - cos (a) sin (a)

2倍角の公式を使用:

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

sin (x) cos (x) = \frac{sin ( 2 x )}{2}

= 1 - \frac{sin ( 2 a )}{2}

1 - \frac{sin ( 2 a )}{2} = 0

1

を右側に移動します

1 - \frac{sin ( 2 a )}{2} = 0

両辺から

1

を引く

1 - \frac{sin ( 2 a )}{2} - 1 = 0 - 1

簡素化

- \frac{sin ( 2 a )}{2} = - 1

- \frac{sin ( 2 a )}{2} = - 1

以下で両辺を乗じる:

2

- \frac{sin ( 2 a )}{2} = - 1

以下で両辺を乗じる:

2

2 (- \frac{sin ( 2 a )}{2}) = 2 (- 1)

簡素化

- sin (2 a) = - 2

- sin (2 a) = - 2

以下で両辺を割る

- 1

- sin (2 a) = - 2

以下で両辺を割る

- 1

\frac{- sin ( 2 a )}{- 1} = \frac{- 2}{- 1}

簡素化

sin (2 a) = 2

sin (2 a) = 2

- 1 \leq sin (x) \leq 1

以下の解はない : a \in R

グラフ

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