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人気のある三角関数 >

cot^2(x)sec(x)-sec(x)=2cot^2(x)-2

解

cot^{2} (x) sec (x) - sec (x) = 2 cot^{2} (x) - 2

解

x = \frac{3 π}{4} + πn, x = \frac{π}{4} + πn, x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

+1

度

x = 13 5^{\circ} + 18 0^{\circ} n, x = 4 5^{\circ} + 18 0^{\circ} n, x = 6 0^{\circ} + 36 0^{\circ} n, x = 30 0^{\circ} + 36 0^{\circ} n

解答ステップ

cot^{2} (x) sec (x) - sec (x) = 2 cot^{2} (x) - 2

両辺から

2 cot^{2} (x) - 2

を引く

cot^{2} (x) sec (x) - sec (x) - 2 cot^{2} (x) + 2 = 0

因数

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

cot^{2} (x) sec (x) - sec (x) - 2 cot^{2} (x) + 2

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

- 2

を

- 2 cot^{2} (x) + 2 : - 2 (cot^{2} (x) - 1)

からくくり出す

- 2 cot^{2} (x) + 2

共通項をくくり出す

- 2

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

sec (x)

を

cot^{2} (x) sec (x) - sec (x) : sec (x) (cot^{2} (x) - 1)

からくくり出す

cot^{2} (x) sec (x) - sec (x)

共通項をくくり出す

sec (x)

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

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

共通項をくくり出す

cot^{2} (x) - 1

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

因数

cot^{2} (x) - 1 : (cot (x) + 1) (cot (x) - 1)

cot^{2} (x) - 1

1

を書き換え

1^{2}

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

2乗の差の公式を適用する:

x^{2} - y^{2} = (x + y) (x - y)

cot^{2} (x) - 1^{2} = (cot (x) + 1) (cot (x) - 1)

= (cot (x) + 1) (cot (x) - 1)

= (cot (x) + 1) (cot (x) - 1) (sec (x) - 2)

(cot (x) + 1) (cot (x) - 1) (sec (x) - 2) = 0

各部分を別個に解く

cot (x) + 1 = 0 or cot (x) - 1 = 0 or sec (x) - 2 = 0

cot (x) + 1 = 0 : x = \frac{3 π}{4} + πn

cot (x) + 1 = 0

1

を右側に移動します

cot (x) + 1 = 0

両辺から

1

を引く

cot (x) + 1 - 1 = 0 - 1

簡素化

cot (x) = - 1

cot (x) = - 1

以下の一般解

cot (x) = - 1

cot (x)

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} cot (x) \mp \infty 31 \frac{3}{3} 0 - \frac{3}{3} - 1 - 3

x = \frac{3 π}{4} + πn

x = \frac{3 π}{4} + πn

cot (x) - 1 = 0 : x = \frac{π}{4} + πn

cot (x) - 1 = 0

1

を右側に移動します

cot (x) - 1 = 0

両辺に

1

を足す

cot (x) - 1 + 1 = 0 + 1

簡素化

cot (x) = 1

cot (x) = 1

以下の一般解

cot (x) = 1

cot (x)

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} cot (x) \mp \infty 31 \frac{3}{3} 0 - \frac{3}{3} - 1 - 3

x = \frac{π}{4} + πn

x = \frac{π}{4} + πn

sec (x) - 2 = 0 : x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

sec (x) - 2 = 0

2

を右側に移動します

sec (x) - 2 = 0

両辺に

2

を足す

sec (x) - 2 + 2 = 0 + 2

簡素化

sec (x) = 2

sec (x) = 2

以下の一般解

sec (x) = 2

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}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

すべての解を組み合わせる

x = \frac{3 π}{4} + πn, x = \frac{π}{4} + πn, x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

グラフ

人気の例

15sin^2(x)-22sin(x)+8=0

15 sin^{2} (x) - 22 sin (x) + 8 = 0

1.333*sin(48)=sin(x)

1.333 \cdot sin (4 8^{\circ}) = sin (x)

2sin(θ)=2+2cos(θ)

2 sin (θ) = 2 + 2 cos (θ)

sec^2(x)+0.5sec(x)=0

sec^{2} (x) + 0.5 sec (x) = 0

solvefor x,ysin(xy)=y^2+2

so l v e f or x, y sin (x y) = y^{2} + 2