ja

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

人気のある三角関数 >

sec^2(x)-2tan^2(x)= 2/3

解

sec^{2} (x) - 2 tan^{2} (x) = \frac{2}{3}

解

x = \frac{π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn, x = \frac{7 π}{6} + 2 πn

+1

度

x = 3 0^{\circ} + 36 0^{\circ} n, x = 33 0^{\circ} + 36 0^{\circ} n, x = 15 0^{\circ} + 36 0^{\circ} n, x = 21 0^{\circ} + 36 0^{\circ} n

解答ステップ

sec^{2} (x) - 2 tan^{2} (x) = \frac{2}{3}

両辺から

\frac{2}{3}

を引く

sec^{2} (x) - 2 tan^{2} (x) - \frac{2}{3} = 0

簡素化

sec^{2} (x) - 2 tan^{2} (x) - \frac{2}{3} : \frac{3 sec ^{2} ( x ) - 6 tan ^{2} ( x ) - 2}{3}

sec^{2} (x) - 2 tan^{2} (x) - \frac{2}{3}

元を分数に変換する:

sec^{2} (x) = \frac{sec ^{2} ( x ) 3}{3}, 2 tan^{2} (x) = \frac{2 tan ^{2} ( x ) 3}{3}

= \frac{sec ^{2} ( x ) \cdot 3}{3} - \frac{2 tan ^{2} ( x ) \cdot 3}{3} - \frac{2}{3}

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{sec ^{2} ( x ) \cdot 3 - 2 tan ^{2} ( x ) \cdot 3 - 2}{3}

数を乗じる:

2 \cdot 3 = 6

= \frac{3 sec ^{2} ( x ) - 6 tan ^{2} ( x ) - 2}{3}

\frac{3 sec ^{2} ( x ) - 6 tan ^{2} ( x ) - 2}{3} = 0

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

3 sec^{2} (x) - 6 tan^{2} (x) - 2 = 0

三角関数の公式を使用して書き換える

- 2 + 3 sec^{2} (x) - 6 tan^{2} (x)

ピタゴラスの公式を使用する:

tan^{2} (x) + 1 = sec^{2} (x)

tan^{2} (x) = sec^{2} (x) - 1

= - 2 + 3 sec^{2} (x) - 6 (sec^{2} (x) - 1)

簡素化

- 2 + 3 sec^{2} (x) - 6 (sec^{2} (x) - 1) : - 3 sec^{2} (x) + 4

- 2 + 3 sec^{2} (x) - 6 (sec^{2} (x) - 1)

拡張

- 6 (sec^{2} (x) - 1) : - 6 sec^{2} (x) + 6

- 6 (sec^{2} (x) - 1)

分配法則を適用する:

a (b - c) = ab - a c

a = - 6, b = sec^{2} (x), c = 1

= - 6 sec^{2} (x) - (- 6) \cdot 1

マイナス・プラスの規則を適用する

- (- a) = a

= - 6 sec^{2} (x) + 6 \cdot 1

数を乗じる:

6 \cdot 1 = 6

= - 6 sec^{2} (x) + 6

= - 2 + 3 sec^{2} (x) - 6 sec^{2} (x) + 6

簡素化

- 2 + 3 sec^{2} (x) - 6 sec^{2} (x) + 6 : - 3 sec^{2} (x) + 4

- 2 + 3 sec^{2} (x) - 6 sec^{2} (x) + 6

類似した元を足す:

3 sec^{2} (x) - 6 sec^{2} (x) = - 3 sec^{2} (x)

= - 2 - 3 sec^{2} (x) + 6

条件のようなグループ

= - 3 sec^{2} (x) - 2 + 6

数を足す/引く:

- 2 + 6 = 4

= - 3 sec^{2} (x) + 4

= - 3 sec^{2} (x) + 4

= - 3 sec^{2} (x) + 4

4 - 3 sec^{2} (x) = 0

置換で解く

4 - 3 sec^{2} (x) = 0

仮定:

sec (x) = u

4 - 3 u^{2} = 0

4 - 3 u^{2} = 0 : u = \frac{2 3}{3}, u = - \frac{2 3}{3}

4 - 3 u^{2} = 0

4

を右側に移動します

4 - 3 u^{2} = 0

両辺から

4

を引く

4 - 3 u^{2} - 4 = 0 - 4

簡素化

- 3 u^{2} = - 4

- 3 u^{2} = - 4

以下で両辺を割る

- 3

- 3 u^{2} = - 4

以下で両辺を割る

- 3

\frac{- 3 u ^{2}}{- 3} = \frac{- 4}{- 3}

簡素化

u^{2} = \frac{4}{3}

u^{2} = \frac{4}{3}

x^{2} = f (a)

の場合, 解は

x = f (a), - f (a)

u = \frac{4}{3}, u = - \frac{4}{3}

\frac{4}{3} = \frac{2 3}{3}

\frac{4}{3}

累乗根の規則を適用する:

n \frac{a}{b} = \frac{n a}{n b},

, 以下を想定

a \geq 0, b \geq 0

= \frac{4}{3}

4 = 2

4

数を因数に分解する:

4 = 2^{2}

= 2^{2}

累乗根の規則を適用する:

n a^{n} = a

2^{2} = 2

= 2

= \frac{2}{3}

有理化する

\frac{2}{3} : \frac{2 3}{3}

\frac{2}{3}

共役で乗じる

\frac{3}{3}

= \frac{2 3}{3 3}

33 = 3

33

累乗根の規則を適用する:

a a = a

33 = 3

= 3

= \frac{2 3}{3}

= \frac{2 3}{3}

- \frac{4}{3} = - \frac{2 3}{3}

- \frac{4}{3}

簡素化

\frac{4}{3} : \frac{2}{3}

\frac{4}{3}

累乗根の規則を適用する:

n \frac{a}{b} = \frac{n a}{n b},

, 以下を想定

a \geq 0, b \geq 0

= \frac{4}{3}

4 = 2

4

数を因数に分解する:

4 = 2^{2}

= 2^{2}

累乗根の規則を適用する:

n a^{n} = a

2^{2} = 2

= 2

= \frac{2}{3}

= - \frac{2}{3}

有理化する

- \frac{2}{3} : - \frac{2 3}{3}

- \frac{2}{3}

共役で乗じる

\frac{3}{3}

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

33 = 3

33

累乗根の規則を適用する:

a a = a

33 = 3

= 3

= - \frac{2 3}{3}

= - \frac{2 3}{3}

u = \frac{2 3}{3}, u = - \frac{2 3}{3}

代用を戻す

u = sec (x)

sec (x) = \frac{2 3}{3}, sec (x) = - \frac{2 3}{3}

sec (x) = \frac{2 3}{3}, sec (x) = - \frac{2 3}{3}

sec (x) = \frac{2 3}{3} : x = \frac{π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

sec (x) = \frac{2 3}{3}

以下の一般解

sec (x) = \frac{2 3}{3}

sec (x)

2 πn

循環を含む周期性テーブル :

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sec (x) 1 \frac{2 3}{3} 22 Undefined - 2 - 2 - \frac{2 3}{3} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sec (x) - 1 - \frac{2 3}{3} - 2 - 2 Undefined 22 \frac{2 3}{3}

x = \frac{π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

x = \frac{π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

sec (x) = - \frac{2 3}{3} : x = \frac{5 π}{6} + 2 πn, x = \frac{7 π}{6} + 2 πn

sec (x) = - \frac{2 3}{3}

以下の一般解

sec (x) = - \frac{2 3}{3}

sec (x)

2 πn

循環を含む周期性テーブル :

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sec (x) 1 \frac{2 3}{3} 22 Undefined - 2 - 2 - \frac{2 3}{3} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sec (x) - 1 - \frac{2 3}{3} - 2 - 2 Undefined 22 \frac{2 3}{3}

x = \frac{5 π}{6} + 2 πn, x = \frac{7 π}{6} + 2 πn

x = \frac{5 π}{6} + 2 πn, x = \frac{7 π}{6} + 2 πn

すべての解を組み合わせる

x = \frac{π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn, x = \frac{7 π}{6} + 2 πn

グラフ

人気の例

cos^2(x)-3cos(x)-1=0

cos^{2} (x) - 3 cos (x) - 1 = 0

cos(3x)=-sin(x+pi/6)

cos (3 x) = - sin (x + \frac{π}{6})

sin (θ) = \frac{7}{10}

tan (5 x) = 1

sec (5 x) = 2