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人気のある三角関数 >

tan(x)+2cos(x)csc(x)=sec(x)cos(x)+cot(x)

解

tan (x) + 2 cos (x) csc (x) = sec (x) cos (x) + cot (x)

解

以下の解はない : x \in R

解答ステップ

tan (x) + 2 cos (x) csc (x) = sec (x) cos (x) + cot (x)

両辺から

sec (x) cos (x) + cot (x)

を引く

tan (x) + 2 cos (x) csc (x) - sec (x) cos (x) - cot (x) = 0

サイン, コサインで表わす

- cot (x) + tan (x) - cos (x) sec (x) + 2 cos (x) csc (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) - cos (x) sec (x) + 2 cos (x) csc (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 )} + \frac{sin ( x )}{cos ( x )} - cos (x) sec (x) + 2 cos (x) csc (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 )} + \frac{sin ( x )}{cos ( x )} - cos (x) \frac{1}{cos ( x )} + 2 cos (x) csc (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 )} + \frac{sin ( x )}{cos ( x )} - cos (x) \frac{1}{cos ( x )} + 2 cos (x) \frac{1}{sin ( x )}

簡素化

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

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

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

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

分数を乗じる:

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

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

共通因数を約分する:

cos (x)

= 1

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

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

分数を乗じる:

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

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

数を乗じる:

1 \cdot 2 = 2

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

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

分数を組み合わせる

- \frac{cos ( x )}{sin ( x )} + \frac{2 cos ( x )}{sin ( x )} : \frac{cos ( x )}{sin ( x )}

規則を適用

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

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

類似した元を足す:

- cos (x) + 2 cos (x) = cos (x)

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

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

元を分数に変換する:

1 = \frac{1}{1}

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

以下の最小公倍数:

sin (x), cos (x), 1 : sin (x) cos (x)

sin (x), cos (x), 1

最小公倍数 (LCM)

因数分解された式の 1 つ以上に合わられる因数で構成された式を計算する

= sin (x) cos (x)

LCMに基づいて分数を調整する

該当する分母を乗じてLCMに変えるために

必要な量で各分子を乗じる

sin (x) cos (x)

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

の場合

:

分母と分子に以下を乗じる:

cos (x)

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

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

の場合

:

分母と分子に以下を乗じる:

sin (x)

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

\frac{1}{1}

の場合

:

分母と分子に以下を乗じる:

sin (x) cos (x)

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

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

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

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

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

cos^{2} (x) + sin^{2} (x) - cos (x) sin (x) = 0

三角関数の公式を使用して書き換える

- cos (x) sin (x) + 1

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

両辺から

1

を引く

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

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

簡素化

- sin (2 x) = - 2

- sin (2 x) = - 2

以下で両辺を割る

- 1

- sin (2 x) = - 2

以下で両辺を割る

- 1

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

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 (x) = 1.22719

cos(a)=(sqrt(5))/5

cos (a) = \frac{5}{5}

5sec^2(x)-5=0,0<= x<2pi

5 sec^{2} (x) - 5 = 0, 0 \leq x < 2 π

2 sin (5 x) + 3 = 2

5sin(y)-5=3sin(y)-4

5 sin (y) - 5 = 3 sin (y) - 4