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人気のある三角関数 >

2cot(x)cos(x)+2cos(x)=cot(x)+1

解

2 cot (x) cos (x) + 2 cos (x) = cot (x) + 1

解

x = \frac{3 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 = 6 0^{\circ} + 36 0^{\circ} n, x = 30 0^{\circ} + 36 0^{\circ} n

解答ステップ

2 cot (x) cos (x) + 2 cos (x) = cot (x) + 1

両辺から

cot (x) + 1

を引く

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

因数

2 cot (x) cos (x) + 2 cos (x) - cot (x) - 1 : (cot (x) + 1) (2 cos (x) - 1)

2 cot (x) cos (x) + 2 cos (x) - cot (x) - 1

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

- 1

を

- cot (x) - 1 : - (cot (x) + 1)

からくくり出す

- cot (x) - 1

共通項をくくり出す

- 1

= - (cot (x) + 1)

2 cos (x)

を

2 cot (x) cos (x) + 2 cos (x) : 2 cos (x) (cot (x) + 1)

からくくり出す

2 cot (x) cos (x) + 2 cos (x)

共通項をくくり出す

2 cos (x)

= 2 cos (x) (cot (x) + 1)

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

共通項をくくり出す

cot (x) + 1

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

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

各部分を別個に解く

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

2 cos (x) - 1 = 0 : x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

2 cos (x) - 1 = 0

1

を右側に移動します

2 cos (x) - 1 = 0

両辺に

1

を足す

2 cos (x) - 1 + 1 = 0 + 1

簡素化

2 cos (x) = 1

2 cos (x) = 1

以下で両辺を割る

2

2 cos (x) = 1

以下で両辺を割る

2

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

簡素化

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

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

以下の一般解

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

cos (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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} 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} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

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}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

グラフ

人気の例

tan(θ)-7=-12cot(θ)

tan (θ) - 7 = - 12 cot (θ)

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

6sin(b)+sqrt(12)=0

6 sin (b) + 12 = 0

tan(x)+sec(x)-1=0

tan (x) + sec (x) - 1 = 0

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

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