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人気のある三角関数 >

(sec(B)+csc(B))/(1+tan(B))=csc^2(B)

解

\frac{sec ( B ) + csc ( B )}{1 + tan ( B )} = csc^{2} (B)

解

以下の解はない : B \in R

解答ステップ

\frac{sec ( B ) + csc ( B )}{1 + tan ( B )} = csc^{2} (B)

両辺から

csc^{2} (B)

を引く

\frac{sec ( B ) + csc ( B )}{1 + tan ( B )} - csc^{2} (B) = 0

簡素化

\frac{sec ( B ) + csc ( B )}{1 + tan ( B )} - csc^{2} (B) : \frac{sec ( B ) + csc ( B ) - csc ^{2} ( B ) ( 1 + tan ( B ) )}{1 + tan ( B )}

\frac{sec ( B ) + csc ( B )}{1 + tan ( B )} - csc^{2} (B)

元を分数に変換する:

csc^{2} (B) = \frac{csc ^{2} ( B ) ( 1 + tan ( B ) )}{1 + tan ( B )}

= \frac{sec ( B ) + csc ( B )}{1 + tan ( B )} - \frac{csc ^{2} ( B ) ( 1 + tan ( B ) )}{1 + tan ( B )}

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 ( B ) + csc ( B ) - csc ^{2} ( B ) ( 1 + tan ( B ) )}{1 + tan ( B )}

\frac{sec ( B ) + csc ( B ) - csc ^{2} ( B ) ( 1 + tan ( B ) )}{1 + tan ( B )} = 0

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

sec (B) + csc (B) - csc^{2} (B) (1 + tan (B)) = 0

サイン, コサインで表わす

csc (B) + sec (B) - (1 + tan (B)) csc^{2} (B)

基本的な三角関数の公式を使用する:

csc (x) = \frac{1}{sin ( x )}

= \frac{1}{sin ( B )} + sec (B) - (1 + tan (B)) (\frac{1}{sin ( B )})^{2}

基本的な三角関数の公式を使用する:

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

= \frac{1}{sin ( B )} + \frac{1}{cos ( B )} - (1 + tan (B)) (\frac{1}{sin ( B )})^{2}

基本的な三角関数の公式を使用する:

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

= \frac{1}{sin ( B )} + \frac{1}{cos ( B )} - (1 + \frac{sin ( B )}{cos ( B )}) (\frac{1}{sin ( B )})^{2}

簡素化

\frac{1}{sin ( B )} + \frac{1}{cos ( B )} - (1 + \frac{sin ( B )}{cos ( B )}) (\frac{1}{sin ( B )})^{2} : \frac{sin ( B ) cos ( B ) + sin ^{2} ( B ) - cos ( B ) - sin ( B )}{sin ^{2} ( B ) cos ( B )}

\frac{1}{sin ( B )} + \frac{1}{cos ( B )} - (1 + \frac{sin ( B )}{cos ( B )}) (\frac{1}{sin ( B )})^{2}

(1 + \frac{sin ( B )}{cos ( B )}) (\frac{1}{sin ( B )})^{2} = \frac{cos ( B ) + sin ( B )}{sin ^{2} ( B ) cos ( B )}

(1 + \frac{sin ( B )}{cos ( B )}) (\frac{1}{sin ( B )})^{2}

結合

1 + \frac{sin ( B )}{cos ( B )} : \frac{cos ( B ) + sin ( B )}{cos ( B )}

1 + \frac{sin ( B )}{cos ( B )}

元を分数に変換する:

1 = \frac{1 cos ( B )}{cos ( B )}

= \frac{1 \cdot cos ( B )}{cos ( B )} + \frac{sin ( B )}{cos ( B )}

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{1 \cdot cos ( B ) + sin ( B )}{cos ( B )}

乗算:

1 \cdot cos (B) = cos (B)

= \frac{cos ( B ) + sin ( B )}{cos ( B )}

= (\frac{1}{sin ( B )})^{2} \frac{cos ( B ) + sin ( B )}{cos ( B )}

(\frac{1}{sin ( B )})^{2} = \frac{1}{sin ^{2} ( B )}

(\frac{1}{sin ( B )})^{2}

指数の規則を適用する:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{1 ^{2}}{sin ^{2} ( B )}

規則を適用

1^{a} = 1

1^{2} = 1

= \frac{1}{sin ^{2} ( B )}

= \frac{cos ( B ) + sin ( B )}{cos ( B )} \cdot \frac{1}{sin ^{2} ( B )}

分数を乗じる:

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

= \frac{( cos ( B ) + sin ( B ) ) \cdot 1}{cos ( B ) sin ^{2} ( B )}

(cos (B) + sin (B)) \cdot 1 = cos (B) + sin (B)

(cos (B) + sin (B)) \cdot 1

乗算:

(cos (B) + sin (B)) \cdot 1 = (cos (B) + sin (B))

= (cos (B) + sin (B))

括弧を削除する:

(a) = a

= cos (B) + sin (B)

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

= \frac{1}{sin ( B )} + \frac{1}{cos ( B )} - \frac{cos ( B ) + sin ( B )}{sin ^{2} ( B ) cos ( B )}

以下の最小公倍数:

sin (B), cos (B), cos (B) sin^{2} (B) : sin^{2} (B) cos (B)

sin (B), cos (B), cos (B) sin^{2} (B)

最小公倍数 (LCM)

因数分解された式の 1 つ以上に合わられる因数で構成された式を計算する

= sin^{2} (B) cos (B)

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^{2} (B) cos (B)

\frac{1}{sin ( B )}

の場合

:

分母と分子に以下を乗じる:

sin (B) cos (B)

\frac{1}{sin ( B )} = \frac{1 \cdot sin ( B ) cos ( B )}{sin ( B ) sin ( B ) cos ( B )} = \frac{sin ( B ) cos ( B )}{sin ^{2} ( B ) cos ( B )}

\frac{1}{cos ( B )}

の場合

:

分母と分子に以下を乗じる:

sin^{2} (B)

\frac{1}{cos ( B )} = \frac{1 \cdot sin ^{2} ( B )}{cos ( B ) sin ^{2} ( B )} = \frac{sin ^{2} ( B )}{sin ^{2} ( B ) cos ( B )}

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

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{sin ( B ) cos ( B ) + sin ^{2} ( B ) - ( cos ( B ) + sin ( B ) )}{sin ^{2} ( B ) cos ( B )}

- (cos (B) + sin (B)) : - cos (B) - sin (B)

- (cos (B) + sin (B))

括弧を分配する

= - (cos (B)) - (sin (B))

マイナス・プラスの規則を適用する

+ (- a) = - a

= - cos (B) - sin (B)

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

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

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

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

- cos (B) - sin (B) + sin^{2} (B) + cos (B) sin (B) = 0

因数

- cos (B) - sin (B) + sin^{2} (B) + cos (B) sin (B) : (sin (B) + cos (B)) (sin (B) - 1)

- cos (B) - sin (B) + sin^{2} (B) + cos (B) sin (B)

= (- sin (B) - cos (B)) + (sin^{2} (B) + sin (B) cos (B))

sin (B)

を

sin^{2} (B) + sin (B) cos (B) : sin (B) (sin (B) + cos (B))

からくくり出す

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

指数の規則を適用する:

a^{b + c} = a^{b} a^{c}

sin^{2} (B) = sin (B) sin (B)

= sin (B) sin (B) + sin (B) cos (B)

共通項をくくり出す

sin (B)

= sin (B) (sin (B) + cos (B))

- 1

を

- sin (B) - cos (B) : - (sin (B) + cos (B))

からくくり出す

- sin (B) - cos (B)

共通項をくくり出す

- 1

= - (sin (B) + cos (B))

= sin (B) (sin (B) + cos (B)) - (sin (B) + cos (B))

共通項をくくり出す

sin (B) + cos (B)

= (sin (B) + cos (B)) (sin (B) - 1)

(sin (B) + cos (B)) (sin (B) - 1) = 0

各部分を別個に解く

sin (B) + cos (B) = 0 or sin (B) - 1 = 0

sin (B) + cos (B) = 0 : B = \frac{3 π}{4} + πn

sin (B) + cos (B) = 0

三角関数の公式を使用して書き換える

sin (B) + cos (B) = 0

cos (B), cos (B) \neq = 0

で両辺を割る

\frac{sin ( B ) + cos ( B )}{cos ( B )} = \frac{0}{cos ( B )}

簡素化

\frac{sin ( B )}{cos ( B )} + 1 = 0

基本的な三角関数の公式を使用する:

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

tan (B) + 1 = 0

tan (B) + 1 = 0

1

を右側に移動します

tan (B) + 1 = 0

両辺から

1

を引く

tan (B) + 1 - 1 = 0 - 1

簡素化

tan (B) = - 1

tan (B) = - 1

以下の一般解

tan (B) = - 1

tan (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} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

B = \frac{3 π}{4} + πn

B = \frac{3 π}{4} + πn

sin (B) - 1 = 0 : B = \frac{π}{2} + 2 πn

sin (B) - 1 = 0

1

を右側に移動します

sin (B) - 1 = 0

両辺に

1

を足す

sin (B) - 1 + 1 = 0 + 1

簡素化

sin (B) = 1

sin (B) = 1

以下の一般解

sin (B) = 1

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

B = \frac{π}{2} + 2 πn

B = \frac{π}{2} + 2 πn

すべての解を組み合わせる

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

equationは以下で未定義のため:

\frac{3 π}{4} + πn, \frac{π}{2} + 2 πn

以下の解はない : B \in R

グラフ

人気の例

4=sqrt(2)csc(3x)

4 = 2 csc (3 x)

21=24+8cos((pix)/6)

21 = 24 + 8 cos (\frac{π x}{6})

sin(x)=(16sin(31))/(12)

sin (x) = \frac{16 sin ( 3 1 ^{\circ} )}{12}

sinh(z)-cosh(z)=0

sinh (z) - cosh (z) = 0

cos(x)=-1.588908648

cos (x) = - 1.588908648