ja

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

人気のある三角関数 >

証明する csc^2(x)-csc^2(x)*cos^2(x)=1

解

証明する

csc^{2} (x) - csc^{2} (x) \cdot cos^{2} (x) = 1

解

真

解答ステップ

csc^{2} (x) - csc^{2} (x) cos^{2} (x) = 1

左側を操作する

csc^{2} (x) - csc^{2} (x) cos^{2} (x)

サイン, コサインで表わす

csc^{2} (x) - cos^{2} (x) csc^{2} (x)

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

簡素化

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

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

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

(\frac{1}{sin ( x )})^{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} ( x )}

規則を適用

1^{a} = 1

1^{2} = 1

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

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

cos^{2} (x) (\frac{1}{sin ( x )})^{2}

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

(\frac{1}{sin ( x )})^{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} ( x )}

規則を適用

1^{a} = 1

1^{2} = 1

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

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

分数を乗じる:

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

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

乗算:

1 \cdot cos^{2} (x) = cos^{2} (x)

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

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

規則を適用

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

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

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

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

三角関数の公式を使用して書き換える

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

ピタゴラスの公式を使用する:

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

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

= \frac{sin ^{2} ( x )}{sin ^{2} ( x )}

規則を適用

\frac{a}{a} = 1

= 1

= 1

両辺を同じ形式にできることを証明した

\Rightarrow 真

人気の例

証明する cos(θ)-sin(θ)sin(2θ)=cos(θ)cos(2θ)

p ro v e cos (θ) - sin (θ) sin (2 θ) = cos (θ) cos (2 θ)

証明する 1+(cot(A))^2=*(csc(A))^2

p ro v e 1 + (cot (A))^{2} = \cdot (csc (A))^{2}

証明する (sin(x)*cos(x))/(tan(x))=cos^2(x)

p ro v e \frac{sin ( x ) \cdot cos ( x )}{tan ( x )} = cos^{2} (x)

証明する 1/(cos^2(x))=20

p ro v e \frac{1}{cos ^{2} ( x )} = 20

証明する (1-cos^2(a))/(cos^2(a))=tan^2(a)

p ro v e \frac{1 - cos ^{2} ( a )}{cos ^{2} ( a )} = tan^{2} (a)