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人気のある三角関数 >

tan(x)cot(x)=csc(x)sec(x)

解

tan (x) cot (x) = csc (x) sec (x)

解

以下の解はない : x \in R

解答ステップ

tan (x) cot (x) = csc (x) sec (x)

両辺から

csc (x) sec (x)

を引く

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

サイン, コサインで表わす

cot (x) tan (x) - csc (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 )}

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

基本的な三角関数の公式を使用する:

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

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

基本的な三角関数の公式を使用する:

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

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

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

簡素化

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

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

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

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

共通因数を約分する:

cos (x)

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

共通因数を約分する:

sin (x)

= 1

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

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

数を乗じる:

1 \cdot 1 = 1

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

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

元を分数に変換する:

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

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

乗算:

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

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

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

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

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

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

三角関数の公式を使用して書き換える

- 1 + cos (x) sin (x)

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 x )}{2}

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

1

を右側に移動します

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

両辺に

1

を足す

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

簡素化

\frac{sin ( 2 x )}{2} = 1

\frac{sin ( 2 x )}{2} = 1

以下で両辺を乗じる:

2

\frac{sin ( 2 x )}{2} = 1

以下で両辺を乗じる:

2

\frac{2 sin ( 2 x )}{2} = 1 \cdot 2

簡素化

sin (2 x) = 2

sin (2 x) = 2

- 1 \leq sin (x) \leq 1

以下の解はない : x \in R

グラフ

人気の例

cos (A) = \frac{3}{5}

cos^2(x)-sin^2(x)= 1/(sqrt(2))

cos^{2} (x) - sin^{2} (x) = \frac{1}{2}

arctan(2x)+arctan(x)= pi/2

arctan (2 x) + arctan (x) = \frac{π}{2}

2cos(x)-5=3cos(x)-4

2 cos (x) - 5 = 3 cos (x) - 4

pi/2 =arctan(x)

\frac{π}{2} = arctan (x)