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人気のある三角関数 >

3sec^2(x)=sec(x)

解

3 sec^{2} (x) = sec (x)

解

以下の解はない : x \in R

解答ステップ

3 sec^{2} (x) = sec (x)

置換で解く

3 sec^{2} (x) = sec (x)

仮定:

sec (x) = u

3 u^{2} = u

3 u^{2} = u : u = \frac{1}{3}, u = 0

3 u^{2} = u

u

を左側に移動します

3 u^{2} = u

両辺から

u

を引く

3 u^{2} - u = u - u

簡素化

3 u^{2} - u = 0

3 u^{2} - u = 0

解くとthe二次式

3 u^{2} - u = 0

二次Equationの公式:

次の場合:

a = 3, b = - 1, c = 0

u_{1, 2} = \frac{- ( - 1 ) \pm ( - 1 ) ^{2} - 4 \cdot 3 \cdot 0}{2 \cdot 3}

u_{1, 2} = \frac{- ( - 1 ) \pm ( - 1 ) ^{2} - 4 \cdot 3 \cdot 0}{2 \cdot 3}

(- 1)^{2} - 4 \cdot 3 \cdot 0 = 1

(- 1)^{2} - 4 \cdot 3 \cdot 0

(- 1)^{2} = 1

(- 1)^{2}

指数の規則を適用する:

n

が偶数であれば

(- a)^{n} = a^{n}

(- 1)^{2} = 1^{2}

= 1^{2}

規則を適用

1^{a} = 1

= 1

4 \cdot 3 \cdot 0 = 0

4 \cdot 3 \cdot 0

規則を適用

0 \cdot a = 0

= 0

= 1 - 0

数を引く:

1 - 0 = 1

= 1

規則を適用

1 = 1

= 1

u_{1, 2} = \frac{- ( - 1 ) \pm 1}{2 \cdot 3}

解を分離する

u_{1} = \frac{- ( - 1 ) + 1}{2 \cdot 3}, u_{2} = \frac{- ( - 1 ) - 1}{2 \cdot 3}

u = \frac{- ( - 1 ) + 1}{2 \cdot 3} : \frac{1}{3}

\frac{- ( - 1 ) + 1}{2 \cdot 3}

規則を適用

- (- a) = a

= \frac{1 + 1}{2 \cdot 3}

数を足す:

1 + 1 = 2

= \frac{2}{2 \cdot 3}

数を乗じる:

2 \cdot 3 = 6

= \frac{2}{6}

共通因数を約分する:

2

= \frac{1}{3}

u = \frac{- ( - 1 ) - 1}{2 \cdot 3} : 0

\frac{- ( - 1 ) - 1}{2 \cdot 3}

規則を適用

- (- a) = a

= \frac{1 - 1}{2 \cdot 3}

数を引く:

1 - 1 = 0

= \frac{0}{2 \cdot 3}

数を乗じる:

2 \cdot 3 = 6

= \frac{0}{6}

規則を適用

\frac{0}{a} = 0, a \neq = 0

= 0

二次equationの解:

u = \frac{1}{3}, u = 0

代用を戻す

u = sec (x)

sec (x) = \frac{1}{3}, sec (x) = 0

sec (x) = \frac{1}{3}, sec (x) = 0

sec (x) = \frac{1}{3} :

解なし

sec (x) = \frac{1}{3}

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

解なし

sec (x) = 0 :

解なし

sec (x) = 0

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

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

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