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 7(cot^2(x))/(csc(x))sec^2(x)=7tan(x)cos(x)csc^2(x)

解

証明する

7 \frac{cot ^{2} ( x )}{csc ( x )} sec^{2} (x) = 7 tan (x) cos (x) csc^{2} (x)

解

真

解答ステップ

7 \cdot \frac{cot ^{2} ( x )}{csc ( x )} sec^{2} (x) = 7 tan (x) cos (x) csc^{2} (x)

左側を操作する

7 \frac{cot ^{2} ( x )}{csc ( x )} sec^{2} (x)

サイン, コサインで表わす

7 \cdot \frac{cot ^{2} ( x )}{csc ( x )} sec^{2} (x)

基本的な三角関数の公式を使用する:

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

= 7 \cdot \frac{( \frac{c o s ( x )}{s i n ( x )} ) ^{2}}{csc ( x )} sec^{2} (x)

基本的な三角関数の公式を使用する:

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

= 7 \cdot \frac{( \frac{c o s ( x )}{s i n ( x )} ) ^{2}}{\frac{1}{s i n ( x )}} sec^{2} (x)

基本的な三角関数の公式を使用する:

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

= 7 \cdot \frac{( \frac{c o s ( x )}{s i n ( x )} ) ^{2}}{\frac{1}{s i n ( x )}} (\frac{1}{cos ( x )})^{2}

簡素化

7 \cdot \frac{( \frac{c o s ( x )}{s i n ( x )} ) ^{2}}{\frac{1}{s i n ( x )}} (\frac{1}{cos ( x )})^{2} : \frac{7}{sin ( x )}

7 \cdot \frac{( \frac{c o s ( x )}{s i n ( x )} ) ^{2}}{\frac{1}{s i n ( x )}} (\frac{1}{cos ( x )})^{2}

分数を乗じる:

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

= \frac{( \frac{c o s ( x )}{s i n ( x )} ) ^{2} \cdot 7 ( \frac{1}{c o s ( x )} ) ^{2}}{\frac{1}{s i n ( x )}}

分数の規則を適用する:

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

= \frac{( \frac{c o s ( x )}{s i n ( x )} ) ^{2} \cdot 7 ( \frac{1}{c o s ( x )} ) ^{2} sin ( x )}{1}

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

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

指数の規則を適用する:

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

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

= \frac{7 ( \frac{1}{c o s ( x )} ) ^{2} \frac{c o s ^{2} ( x )}{s i n ^{2} ( x )} sin ( x )}{1}

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

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

指数の規則を適用する:

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

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

規則を適用

1^{a} = 1

1^{2} = 1

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

= \frac{7 \cdot \frac{c o s ^{2} ( x )}{s i n ^{2} ( x )} \cdot \frac{1}{c o s ^{2} ( x )} sin ( x )}{1}

乗じる

\frac{cos ^{2} ( x )}{sin ^{2} ( x )} \cdot 7 \cdot \frac{1}{cos ^{2} ( x )} sin (x) : \frac{7}{sin ( x )}

\frac{cos ^{2} ( x )}{sin ^{2} ( x )} \cdot 7 \cdot \frac{1}{cos ^{2} ( x )} sin (x)

分数を乗じる:

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

= \frac{cos ^{2} ( x ) \cdot 1 \cdot 7 sin ( x )}{sin ^{2} ( x ) cos ^{2} ( x )}

共通因数を約分する:

cos^{2} (x)

= \frac{1 \cdot 7 sin ( x )}{sin ^{2} ( x )}

数を乗じる:

1 \cdot 7 = 7

= \frac{7 sin ( x )}{sin ^{2} ( x )}

共通因数を約分する:

sin (x)

= \frac{7}{sin ( x )}

= \frac{\frac{7}{s i n ( x )}}{1}

分数の規則を適用する:

\frac{a}{1} = a

= \frac{7}{sin ( x )}

= \frac{7}{sin ( x )}

= \frac{7}{sin ( x )}

右側を操作する

7 tan (x) cos (x) csc^{2} (x)

サイン, コサインで表わす

7 cos (x) csc^{2} (x) tan (x)

基本的な三角関数の公式を使用する:

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

= 7 cos (x) (\frac{1}{sin ( x )})^{2} tan (x)

基本的な三角関数の公式を使用する:

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

= 7 cos (x) (\frac{1}{sin ( x )})^{2} \frac{sin ( x )}{cos ( x )}

簡素化

7 cos (x) (\frac{1}{sin ( x )})^{2} \frac{sin ( x )}{cos ( x )} : \frac{7}{sin ( x )}

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

分数を乗じる:

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

= \frac{sin ( x ) \cdot 7 cos ( x ) ( \frac{1}{s i n ( x )} ) ^{2}}{cos ( x )}

共通因数を約分する:

cos (x)

= sin (x) \cdot 7 (\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 )}

= 7 \cdot \frac{1}{sin ^{2} ( x )} sin (x)

分数を乗じる:

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

= \frac{1 \cdot sin ( x ) \cdot 7}{sin ^{2} ( x )}

数を乗じる:

1 \cdot 7 = 7

= \frac{7 sin ( x )}{sin ^{2} ( x )}

共通因数を約分する:

sin (x)

= \frac{7}{sin ( x )}

= \frac{7}{sin ( x )}

= \frac{7}{sin ( x )}

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^2(x)=1+sin^2(x)

p ro v e cos^{2} (x) = 1 + sin^{2} (x)

証明する cos^2(x)(2+tan^2(x))=2-sin^2(x)

p ro v e cos^{2} (x) (2 + tan^{2} (x)) = 2 - sin^{2} (x)

証明する sin(x)(1+cos(2x))=sin(2x)cos(x)

p ro v e sin (x) (1 + cos (2 x)) = sin (2 x) cos (x)

証明する (sec(x)-tan(x))(1+sin(x))=cos(x)

p ro v e (sec (x) - tan (x)) (1 + sin (x)) = cos (x)

証明する tan(-x)=cos(x)

p ro v e tan (- x) = cos (x)