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人気のある三角関数 >

(1+tan^2(x))/(1+sec(x))=sec(x)

解

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

解

以下の解はない : x \in R

解答ステップ

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

両辺から

sec (x)

を引く

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

簡素化

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

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

元を分数に変換する:

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

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

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

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

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

三角関数の公式を使用して書き換える

1 + tan^{2} (x) - (1 + sec (x)) sec (x)

ピタゴラスの公式を使用する:

tan^{2} (x) + 1 = sec^{2} (x)

= - sec (x) (1 + sec (x)) + sec^{2} (x)

簡素化

- sec (x) (1 + sec (x)) + sec^{2} (x) : - sec (x)

- sec (x) (1 + sec (x)) + sec^{2} (x)

拡張

- sec (x) (1 + sec (x)) : - sec (x) - sec^{2} (x)

- sec (x) (1 + sec (x))

分配法則を適用する:

a (b + c) = ab + a c

a = - sec (x), b = 1, c = sec (x)

= - sec (x) \cdot 1 + (- sec (x)) sec (x)

マイナス・プラスの規則を適用する

+ (- a) = - a

= - 1 \cdot sec (x) - sec (x) sec (x)

簡素化

- 1 \cdot sec (x) - sec (x) sec (x) : - sec (x) - sec^{2} (x)

- 1 \cdot sec (x) - sec (x) sec (x)

1 \cdot sec (x) = sec (x)

1 \cdot sec (x)

乗算:

1 \cdot sec (x) = sec (x)

= sec (x)

sec (x) sec (x) = sec^{2} (x)

sec (x) sec (x)

指数の規則を適用する:

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

sec (x) sec (x) = sec^{1 + 1} (x)

= sec^{1 + 1} (x)

数を足す:

1 + 1 = 2

= sec^{2} (x)

= - sec (x) - sec^{2} (x)

= - sec (x) - sec^{2} (x)

= - sec (x) - sec^{2} (x) + sec^{2} (x)

類似した元を足す:

- sec^{2} (x) + sec^{2} (x) = 0

= - sec (x)

= - sec (x)

- sec (x) = 0

以下で両辺を割る

- 1

- sec (x) = 0

以下で両辺を割る

- 1

\frac{- sec ( x )}{- 1} = \frac{0}{- 1}

簡素化

sec (x) = 0

sec (x) = 0

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

以下の解はない : x \in R

グラフ

人気の例

-sin^2(x)+2cos(x)-2=0

sin^4(x)+cos^2(x)=2