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人気のある三角関数 >

tan(x)=(sec(x))/(cos(x))

解

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

解

以下の解はない : x \in R

解答ステップ

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

両辺から

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

を引く

tan (x) - \frac{sec ( x )}{cos ( x )} = 0

簡素化

tan (x) - \frac{sec ( x )}{cos ( x )} : \frac{tan ( x ) cos ( x ) - sec ( x )}{cos ( x )}

tan (x) - \frac{sec ( x )}{cos ( x )}

元を分数に変換する:

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

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

\frac{tan ( x ) cos ( x ) - sec ( x )}{cos ( x )} = 0

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

tan (x) cos (x) - sec (x) = 0

サイン, コサインで表わす

- sec (x) + cos (x) tan (x)

基本的な三角関数の公式を使用する:

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

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

簡素化

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

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

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

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

分数を乗じる:

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

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

共通因数を約分する:

cos (x)

= sin (x)

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

元を分数に変換する:

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

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

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

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

sin (x) = - 0.707

2sin^2(x)+5sin(x)=0

2 sin^{2} (x) + 5 sin (x) = 0

cos(2x)-7cos(x)-3=0

cos (2 x) - 7 cos (x) - 3 = 0

tan^2(45-x/3)=0.58

tan^{2} (4 5^{\circ} - \frac{x}{3}) = 0.58

- 20 csc (x) = 40