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人気のある三角関数 >

sec(2x)csc(2x)=2csc(2x),0<= x<= 2pi

解

sec (2 x) csc (2 x) = 2 csc (2 x), 0 \leq x \leq 2 π

解

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

+1

度

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

解答ステップ

sec (2 x) csc (2 x) = 2 csc (2 x), 0 \leq x \leq 2 π

両辺から

2 csc (2 x)

を引く

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

因数

sec (2 x) csc (2 x) - 2 csc (2 x) : csc (2 x) (sec (2 x) - 2)

sec (2 x) csc (2 x) - 2 csc (2 x)

共通項をくくり出す

csc (2 x)

= csc (2 x) (sec (2 x) - 2)

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

各部分を別個に解く

csc (2 x) = 0 or sec (2 x) - 2 = 0

csc (2 x) = 0, 0 \leq x \leq 2 π :

解なし

csc (2 x) = 0, 0 \leq x \leq 2 π

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

解なし

sec (2 x) - 2 = 0, 0 \leq x \leq 2 π : x = \frac{π}{6}, x = \frac{5 π}{6}, x = \frac{7 π}{6}, x = \frac{11 π}{6}

sec (2 x) - 2 = 0, 0 \leq x \leq 2 π

2

を右側に移動します

sec (2 x) - 2 = 0

両辺に

2

を足す

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

簡素化

sec (2 x) = 2

sec (2 x) = 2

以下の一般解

sec (2 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}

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

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

解く

2 x = \frac{π}{3} + 2 πn : x = \frac{π}{6} + πn

2 x = \frac{π}{3} + 2 πn

以下で両辺を割る

2

2 x = \frac{π}{3} + 2 πn

以下で両辺を割る

2

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

簡素化

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

簡素化

\frac{2 x}{2} : x

\frac{2 x}{2}

数を割る:

\frac{2}{2} = 1

= x

簡素化

\frac{\frac{π}{3}}{2} + \frac{2 πn}{2} : \frac{π}{6} + πn

\frac{\frac{π}{3}}{2} + \frac{2 πn}{2}

\frac{\frac{π}{3}}{2} = \frac{π}{6}

\frac{\frac{π}{3}}{2}

分数の規則を適用する:

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

= \frac{π}{3 \cdot 2}

数を乗じる:

3 \cdot 2 = 6

= \frac{π}{6}

\frac{2 πn}{2} = πn

\frac{2 πn}{2}

数を割る:

\frac{2}{2} = 1

= πn

= \frac{π}{6} + πn

x = \frac{π}{6} + πn

x = \frac{π}{6} + πn

x = \frac{π}{6} + πn

解く

2 x = \frac{5 π}{3} + 2 πn : x = \frac{5 π}{6} + πn

2 x = \frac{5 π}{3} + 2 πn

以下で両辺を割る

2

2 x = \frac{5 π}{3} + 2 πn

以下で両辺を割る

2

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

簡素化

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

簡素化

\frac{2 x}{2} : x

\frac{2 x}{2}

数を割る:

\frac{2}{2} = 1

= x

簡素化

\frac{\frac{5 π}{3}}{2} + \frac{2 πn}{2} : \frac{5 π}{6} + πn

\frac{\frac{5 π}{3}}{2} + \frac{2 πn}{2}

\frac{\frac{5 π}{3}}{2} = \frac{5 π}{6}

\frac{\frac{5 π}{3}}{2}

分数の規則を適用する:

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

= \frac{5 π}{3 \cdot 2}

数を乗じる:

3 \cdot 2 = 6

= \frac{5 π}{6}

\frac{2 πn}{2} = πn

\frac{2 πn}{2}

数を割る:

\frac{2}{2} = 1

= πn

= \frac{5 π}{6} + πn

x = \frac{5 π}{6} + πn

x = \frac{5 π}{6} + πn

x = \frac{5 π}{6} + πn

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

範囲の解答

0 \leq x \leq 2 π

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

すべての解を組み合わせる

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

グラフ

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