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人気のある三角関数 >

((sin(x)+tan(x)))/(1+cos(x))=m*sec(x)

解

\frac{( sin ( x ) + tan ( x ) )}{1 + cos ( x )} = m \cdot sec (x)

解

x = arcsin (m) + 2 πn, x = π + arcsin (- m) + 2 πn

解答ステップ

\frac{( sin ( x ) + tan ( x ) )}{1 + cos ( x )} = m sec (x)

両辺から

m sec (x)

を引く

\frac{sin ( x ) + tan ( x )}{1 + cos ( x )} - m sec (x) = 0

簡素化

\frac{sin ( x ) + tan ( x )}{1 + cos ( x )} - m sec (x) : \frac{sin ( x ) + tan ( x ) - m sec ( x ) ( 1 + cos ( x ) )}{1 + cos ( x )}

\frac{sin ( x ) + tan ( x )}{1 + cos ( x )} - m sec (x)

元を分数に変換する:

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

= \frac{sin ( x ) + tan ( x )}{1 + cos ( x )} - \frac{m sec ( x ) ( 1 + cos ( x ) )}{1 + cos ( x )}

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 ( x ) + tan ( x ) - m sec ( x ) ( 1 + cos ( x ) )}{1 + cos ( x )}

\frac{sin ( x ) + tan ( x ) - m sec ( x ) ( 1 + cos ( x ) )}{1 + cos ( x )} = 0

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

sin (x) + tan (x) - m sec (x) (1 + cos (x)) = 0

サイン, コサインで表わす

sin (x) + tan (x) - (1 + cos (x)) sec (x) m

基本的な三角関数の公式を使用する:

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

= sin (x) + \frac{sin ( x )}{cos ( x )} - (1 + cos (x)) sec (x) m

基本的な三角関数の公式を使用する:

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

= sin (x) + \frac{sin ( x )}{cos ( x )} - (1 + cos (x)) \frac{1}{cos ( x )} m

簡素化

sin (x) + \frac{sin ( x )}{cos ( x )} - (1 + cos (x)) \frac{1}{cos ( x )} m : \frac{sin ( x ) cos ( x ) + sin ( x ) - m ( 1 + cos ( x ) )}{cos ( x )}

sin (x) + \frac{sin ( x )}{cos ( x )} - (1 + cos (x)) \frac{1}{cos ( x )} m

(1 + cos (x)) \frac{1}{cos ( x )} m = \frac{m ( 1 + cos ( x ) )}{cos ( x )}

(1 + cos (x)) \frac{1}{cos ( x )} m

分数を乗じる:

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

= \frac{1 \cdot ( 1 + cos ( x ) ) m}{cos ( x )}

乗算:

1 \cdot (1 + cos (x)) = (1 + cos (x))

= \frac{m ( cos ( x ) + 1 )}{cos ( x )}

= sin (x) + \frac{sin ( x )}{cos ( x )} - \frac{m ( cos ( x ) + 1 )}{cos ( x )}

分数を組み合わせる

\frac{sin ( x )}{cos ( x )} - \frac{m ( cos ( x ) + 1 )}{cos ( x )} : \frac{sin ( x ) - m ( 1 + cos ( x ) )}{cos ( x )}

規則を適用

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

= \frac{sin ( x ) - m ( cos ( x ) + 1 )}{cos ( x )}

= sin (x) + \frac{sin ( x ) - m ( cos ( x ) + 1 )}{cos ( x )}

元を分数に変換する:

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

= \frac{sin ( x ) cos ( x )}{cos ( x )} + \frac{sin ( x ) - ( 1 + cos ( x ) ) m}{cos ( x )}

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 ( x ) cos ( x ) + sin ( x ) - ( 1 + cos ( x ) ) m}{cos ( x )}

= \frac{sin ( x ) cos ( x ) + sin ( x ) - m ( 1 + cos ( x ) )}{cos ( x )}

\frac{sin ( x ) - ( 1 + cos ( x ) ) m + cos ( x ) sin ( x )}{cos ( x )} = 0

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

sin (x) - (1 + cos (x)) m + cos (x) sin (x) = 0

因数

sin (x) - (1 + cos (x)) m + cos (x) sin (x) : (1 + cos (x)) (sin (x) - m)

sin (x) - (1 + cos (x)) m + cos (x) sin (x)

共通項をくくり出す

sin (x)

= sin (x) (1 + cos (x)) - (1 + cos (x)) m

共通項をくくり出す

(1 + cos (x))

= (1 + cos (x)) (sin (x) - m)

(1 + cos (x)) (sin (x) - m) = 0

各部分を別個に解く

1 + cos (x) = 0 or sin (x) - m = 0

1 + cos (x) = 0 : x = π + 2 πn

1 + cos (x) = 0

1

を右側に移動します

1 + cos (x) = 0

両辺から

1

を引く

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

簡素化

cos (x) = - 1

cos (x) = - 1

以下の一般解

cos (x) = - 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}

x = π + 2 πn

x = π + 2 πn

sin (x) - m = 0 : x = arcsin (m) + 2 πn, x = π + arcsin (- m) + 2 πn

sin (x) - m = 0

m

を右側に移動します

sin (x) - m = 0

両辺に

m

を足す

sin (x) - m + m = 0 + m

簡素化

sin (x) = m

sin (x) = m

三角関数の逆数プロパティを適用する

sin (x) = m

以下の一般解

sin (x) = m

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π + arcsin (a) + 2 πn

x = arcsin (m) + 2 πn, x = π + arcsin (- m) + 2 πn

x = arcsin (m) + 2 πn, x = π + arcsin (- m) + 2 πn

すべての解を組み合わせる

x = π + 2 πn, x = arcsin (m) + 2 πn, x = π + arcsin (- m) + 2 πn

equationは以下で未定義のため:

π + 2 πn

x = arcsin (m) + 2 πn, x = π + arcsin (- m) + 2 πn

グラフ

人気の例

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