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 sin^2(a)+sin^2(a)tan^2(a)=tan^2(a)

解

証明する

sin^{2} (a) + sin^{2} (a) tan^{2} (a) = tan^{2} (a)

解

真

解答ステップ

sin^{2} (a) + sin^{2} (a) tan^{2} (a) = tan^{2} (a)

左側を操作する

sin^{2} (a) + sin^{2} (a) tan^{2} (a)

三角関数の公式を使用して書き換える

sin^{2} (a) + sin^{2} (a) tan^{2} (a)

ピタゴラスの公式を使用する:

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

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

= sin^{2} (a) + sin^{2} (a) (sec^{2} (a) - 1)

簡素化

sin^{2} (a) + sin^{2} (a) (sec^{2} (a) - 1) : sin^{2} (a) sec^{2} (a)

sin^{2} (a) + sin^{2} (a) (sec^{2} (a) - 1)

拡張

sin^{2} (a) (sec^{2} (a) - 1) : sin^{2} (a) sec^{2} (a) - sin^{2} (a)

sin^{2} (a) (sec^{2} (a) - 1)

分配法則を適用する:

a (b - c) = ab - a c

a = sin^{2} (a), b = sec^{2} (a), c = 1

= sin^{2} (a) sec^{2} (a) - sin^{2} (a) \cdot 1

= sin^{2} (a) sec^{2} (a) - 1 \cdot sin^{2} (a)

乗算:

1 \cdot sin^{2} (a) = sin^{2} (a)

= sin^{2} (a) sec^{2} (a) - sin^{2} (a)

= sin^{2} (a) + sin^{2} (a) sec^{2} (a) - sin^{2} (a)

類似した元を足す:

sin^{2} (a) - sin^{2} (a) = 0

= sin^{2} (a) sec^{2} (a)

= sin^{2} (a) sec^{2} (a)

= sin^{2} (a) sec^{2} (a)

サイン, コサインで表わす

sec^{2} (a) sin^{2} (a)

基本的な三角関数の公式を使用する:

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

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

簡素化

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

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

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

(\frac{1}{cos ( a )})^{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} ( a )}

規則を適用

1^{a} = 1

1^{2} = 1

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

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

分数を乗じる:

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

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

乗算:

1 \cdot sin^{2} (a) = sin^{2} (a)

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

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

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

三角関数の公式を使用して書き換える

= \frac{sin ( a )}{cos ( a )} \cdot \frac{sin ( a )}{cos ( a )}

基本的な三角関数の公式を使用する:

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

\frac{sin ( a ) tan ( a )}{cos ( a )}

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

基本的な三角関数の公式を使用する:

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

tan (a) tan (a)

簡素化

tan (a) tan (a) : tan^{2} (a)

tan (a) tan (a)

指数の規則を適用する:

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

tan (a) tan (a) = tan^{1 + 1} (a)

= tan^{1 + 1} (a)

数を足す:

1 + 1 = 2

= tan^{2} (a)

tan^{2} (a)

tan^{2} (a)

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 sin(b)+cos(b)cot(b)=csc(b)

p ro v e sin (b) + cos (b) cot (b) = csc (b)

証明する (sec(x)-cos(x))/(sin^2(x))=sec(x)

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

証明する (1-cos(2x))/(2sin(x))=sin(x)

p ro v e \frac{1 - cos ( 2 x )}{2 sin ( x )} = sin (x)

証明する tan((3pi)/2-x)=cot(x)

p ro v e tan (\frac{3 π}{2} - x) = cot (x)

証明する (3csc(-x))/(sec(-x))=-3cot(x)

p ro v e \frac{3 csc ( - x )}{sec ( - x )} = - 3 cot (x)