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 >

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

解

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

解

以下の解はない : x \in R

解答ステップ

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

両辺から

cos^{2} (x)

を引く

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

両辺を2乗する

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

両辺から

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

を引く

sin^{4} (x) - 4 + 4 cos^{2} (x) - cos^{4} (x) = 0

指数の規則を適用する:

a^{b} = a^{2} a^{b - 2}

- 4 - cos^{4} (x) + 4 cos^{2} (x) + sin^{2} (x) sin^{2} (x) = 0

三角関数の公式を使用して書き換える

- 4 - cos^{4} (x) + 4 cos^{2} (x) + sin^{2} (x) sin^{2} (x)

ピタゴラスの公式を使用する:

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

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

= - 4 - cos^{4} (x) + 4 cos^{2} (x) + (1 - cos^{2} (x)) (1 - cos^{2} (x))

簡素化

- 4 - cos^{4} (x) + 4 cos^{2} (x) + (1 - cos^{2} (x)) (1 - cos^{2} (x)) : 2 cos^{2} (x) - 3

- 4 - cos^{4} (x) + 4 cos^{2} (x) + (1 - cos^{2} (x)) (1 - cos^{2} (x))

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

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

指数の規則を適用する:

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

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

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

数を足す:

1 + 1 = 2

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

= - 4 - cos^{4} (x) + 4 cos^{2} (x) + (- cos^{2} (x) + 1)^{2}

(1 - cos^{2} (x))^{2} : 1 - 2 cos^{2} (x) + cos^{4} (x)

完全平方式を適用する:

(a - b)^{2} = a^{2} - 2 ab + b^{2}

a = 1, b = cos^{2} (x)

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

簡素化

1^{2} - 2 \cdot 1 \cdot cos^{2} (x) + (cos^{2} (x))^{2} : 1 - 2 cos^{2} (x) + cos^{4} (x)

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

規則を適用

1^{a} = 1

1^{2} = 1

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

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

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

数を乗じる:

2 \cdot 1 = 2

= 2 cos^{2} (x)

(cos^{2} (x))^{2} = cos^{4} (x)

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

指数の規則を適用する:

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

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

数を乗じる:

2 \cdot 2 = 4

= cos^{4} (x)

= 1 - 2 cos^{2} (x) + cos^{4} (x)

= 1 - 2 cos^{2} (x) + cos^{4} (x)

= - 4 - cos^{4} (x) + 4 cos^{2} (x) + 1 - 2 cos^{2} (x) + cos^{4} (x)

簡素化

- 4 - cos^{4} (x) + 4 cos^{2} (x) + 1 - 2 cos^{2} (x) + cos^{4} (x) : 2 cos^{2} (x) - 3

- 4 - cos^{4} (x) + 4 cos^{2} (x) + 1 - 2 cos^{2} (x) + cos^{4} (x)

条件のようなグループ

= - cos^{4} (x) + 4 cos^{2} (x) - 2 cos^{2} (x) + cos^{4} (x) - 4 + 1

類似した元を足す:

4 cos^{2} (x) - 2 cos^{2} (x) = 2 cos^{2} (x)

= - cos^{4} (x) + 2 cos^{2} (x) + cos^{4} (x) - 4 + 1

類似した元を足す:

- cos^{4} (x) + cos^{4} (x) = 0

= 2 cos^{2} (x) - 4 + 1

数を足す/引く:

- 4 + 1 = - 3

= 2 cos^{2} (x) - 3

= 2 cos^{2} (x) - 3

= 2 cos^{2} (x) - 3

- 3 + 2 cos^{2} (x) = 0

置換で解く

- 3 + 2 cos^{2} (x) = 0

仮定:

cos (x) = u

- 3 + 2 u^{2} = 0

- 3 + 2 u^{2} = 0 : u = \frac{3}{2}, u = - \frac{3}{2}

- 3 + 2 u^{2} = 0

3

を右側に移動します

- 3 + 2 u^{2} = 0

両辺に

3

を足す

- 3 + 2 u^{2} + 3 = 0 + 3

簡素化

2 u^{2} = 3

2 u^{2} = 3

以下で両辺を割る

2

2 u^{2} = 3

以下で両辺を割る

2

\frac{2 u ^{2}}{2} = \frac{3}{2}

簡素化

u^{2} = \frac{3}{2}

u^{2} = \frac{3}{2}

x^{2} = f (a)

の場合, 解は

x = f (a), - f (a)

u = \frac{3}{2}, u = - \frac{3}{2}

代用を戻す

u = cos (x)

cos (x) = \frac{3}{2}, cos (x) = - \frac{3}{2}

cos (x) = \frac{3}{2}, cos (x) = - \frac{3}{2}

cos (x) = \frac{3}{2} :

解なし

cos (x) = \frac{3}{2}

- 1 \leq cos (x) \leq 1

解なし

cos (x) = - \frac{3}{2} :

解なし

cos (x) = - \frac{3}{2}

- 1 \leq cos (x) \leq 1

解なし

すべての解を組み合わせる

解なし

元のequationに当てはめて解を検算する

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

に当てはめて解を確認する

equationに一致しないものを削除する。

以下の解はない : x \in R

グラフ

人気の例

cot((2θ)/3)=-sqrt(3)

cot (\frac{2 θ}{3}) = - 3

-3sin(2θ)=5cos(2θ),0<= 2θ<720

- 3 sin (2 θ) = 5 cos (2 θ), 0^{\circ} \leq 2 θ < 72 0^{\circ}

sin (4 x) = 1

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

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

3cos(x)tan(x)+tan(x)=0

3 cos (x) tan (x) + tan (x) = 0