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人気のある三角関数 >

2/(tan(a)+cot(a))=2sin(a)

解

\frac{2}{tan ( a ) + cot ( a )} = 2 sin (a)

解

以下の解はない : a \in R

解答ステップ

\frac{2}{tan ( a ) + cot ( a )} = 2 sin (a)

両辺から

2 sin (a)

を引く

\frac{2}{tan ( a ) + cot ( a )} - 2 sin (a) = 0

簡素化

\frac{2}{tan ( a ) + cot ( a )} - 2 sin (a) : \frac{2 - 2 sin ( a ) ( tan ( a ) + cot ( a ) )}{tan ( a ) + cot ( a )}

\frac{2}{tan ( a ) + cot ( a )} - 2 sin (a)

元を分数に変換する:

2 sin (a) = \frac{2 sin ( a ) ( tan ( a ) + cot ( a ) )}{tan ( a ) + cot ( a )}

= \frac{2}{tan ( a ) + cot ( a )} - \frac{2 sin ( a ) ( tan ( a ) + cot ( a ) )}{tan ( a ) + cot ( a )}

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{2 - 2 sin ( a ) ( tan ( a ) + cot ( a ) )}{tan ( a ) + cot ( a )}

\frac{2 - 2 sin ( a ) ( tan ( a ) + cot ( a ) )}{tan ( a ) + cot ( a )} = 0

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

2 - 2 sin (a) (tan (a) + cot (a)) = 0

サイン, コサインで表わす

2 - (cot (a) + tan (a)) \cdot 2 sin (a)

基本的な三角関数の公式を使用する:

cot (x) = \frac{cos ( x )}{sin ( x )}

= 2 - (\frac{cos ( a )}{sin ( a )} + tan (a)) \cdot 2 sin (a)

基本的な三角関数の公式を使用する:

tan (x) = \frac{sin ( x )}{cos ( x )}

= 2 - (\frac{cos ( a )}{sin ( a )} + \frac{sin ( a )}{cos ( a )}) \cdot 2 sin (a)

簡素化

2 - (\frac{cos ( a )}{sin ( a )} + \frac{sin ( a )}{cos ( a )}) \cdot 2 sin (a) : \frac{2 cos ( a ) - 2 ( cos ^{2} ( a ) + sin ^{2} ( a ) )}{cos ( a )}

2 - (\frac{cos ( a )}{sin ( a )} + \frac{sin ( a )}{cos ( a )}) \cdot 2 sin (a)

結合

\frac{cos ( a )}{sin ( a )} + \frac{sin ( a )}{cos ( a )} : \frac{cos ^{2} ( a ) + sin ^{2} ( a )}{sin ( a ) cos ( a )}

\frac{cos ( a )}{sin ( a )} + \frac{sin ( a )}{cos ( a )}

以下の最小公倍数:

sin (a), cos (a) : sin (a) cos (a)

sin (a), cos (a)

最小公倍数 (LCM)

sin (a)

または以下のいずれかに現れる因数で構成された式を計算する:

cos (a)

= sin (a) cos (a)

LCMに基づいて分数を調整する

該当する分母を乗じてLCMに変えるために

必要な量で各分子を乗じる

sin (a) cos (a)

\frac{cos ( a )}{sin ( a )}

の場合

:

分母と分子に以下を乗じる:

cos (a)

\frac{cos ( a )}{sin ( a )} = \frac{cos ( a ) cos ( a )}{sin ( a ) cos ( a )} = \frac{cos ^{2} ( a )}{sin ( a ) cos ( a )}

\frac{sin ( a )}{cos ( a )}

の場合

:

分母と分子に以下を乗じる:

sin (a)

\frac{sin ( a )}{cos ( a )} = \frac{sin ( a ) sin ( a )}{cos ( a ) sin ( a )} = \frac{sin ^{2} ( a )}{sin ( a ) cos ( a )}

= \frac{cos ^{2} ( a )}{sin ( a ) cos ( a )} + \frac{sin ^{2} ( a )}{sin ( a ) cos ( a )}

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{cos ^{2} ( a ) + sin ^{2} ( a )}{sin ( a ) cos ( a )}

= 2 - 2 \cdot \frac{cos ^{2} ( a ) + sin ^{2} ( a )}{sin ( a ) cos ( a )} sin (a)

\frac{cos ^{2} ( a ) + sin ^{2} ( a )}{sin ( a ) cos ( a )} \cdot 2 sin (a) = \frac{2 ( cos ^{2} ( a ) + sin ^{2} ( a ) )}{cos ( a )}

\frac{cos ^{2} ( a ) + sin ^{2} ( a )}{sin ( a ) cos ( a )} \cdot 2 sin (a)

分数を乗じる:

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

= \frac{( cos ^{2} ( a ) + sin ^{2} ( a ) ) \cdot 2 sin ( a )}{sin ( a ) cos ( a )}

共通因数を約分する:

sin (a)

= \frac{( cos ^{2} ( a ) + sin ^{2} ( a ) ) \cdot 2}{cos ( a )}

= 2 - \frac{2 ( cos ^{2} ( a ) + sin ^{2} ( a ) )}{cos ( a )}

元を分数に変換する:

2 = \frac{2 cos ( a )}{cos ( a )}

= \frac{2 cos ( a )}{cos ( a )} - \frac{( cos ^{2} ( a ) + sin ^{2} ( a ) ) \cdot 2}{cos ( a )}

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{2 cos ( a ) - ( cos ^{2} ( a ) + sin ^{2} ( a ) ) \cdot 2}{cos ( a )}

= \frac{2 cos ( a ) - 2 ( cos ^{2} ( a ) + sin ^{2} ( a ) )}{cos ( a )}

\frac{- ( cos ^{2} ( a ) + sin ^{2} ( a ) ) \cdot 2 + 2 cos ( a )}{cos ( a )} = 0

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

- (cos^{2} (a) + sin^{2} (a)) \cdot 2 + 2 cos (a) = 0

三角関数の公式を使用して書き換える

- (cos^{2} (a) + sin^{2} (a)) \cdot 2 + 2 cos (a)

ピタゴラスの公式を使用する:

cos^{2} (x) + sin^{2} (x) = 1

= 2 cos (a) - 2 \cdot 1

2 cos (a) - 2 \cdot 1 = 0

数を乗じる:

2 \cdot 1 = 2

2 cos (a) - 2 = 0

2

を右側に移動します

2 cos (a) - 2 = 0

両辺に

2

を足す

2 cos (a) - 2 + 2 = 0 + 2

簡素化

2 cos (a) = 2

2 cos (a) = 2

以下で両辺を割る

2

2 cos (a) = 2

以下で両辺を割る

2

\frac{2 cos ( a )}{2} = \frac{2}{2}

簡素化

cos (a) = 1

cos (a) = 1

以下の一般解

cos (a) = 1

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}

a = 0 + 2 πn

a = 0 + 2 πn

解く

a = 0 + 2 πn : a = 2 πn

a = 0 + 2 πn

0 + 2 πn = 2 πn

a = 2 πn

a = 2 πn

equationは以下で未定義のため:

2 πn

以下の解はない : a \in R

グラフ

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