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人気のある三角関数 >

cos^2(60)+cos^2(45)+cos^2(x)=1

解

cos^{2} (60) + cos^{2} (45) + cos^{2} (x) = 1

解

以下の解はない : x \in R

解答ステップ

cos^{2} (60) + cos^{2} (45) + cos^{2} (x) = 1

置換で解く

cos^{2} (60) + cos^{2} (45) + cos^{2} (x) = 1

仮定:

cos (x) = u

cos^{2} (60) + cos^{2} (45) + u^{2} = 1

cos^{2} (60) + cos^{2} (45) + u^{2} = 1 : u = i - 1 + cos^{2} (60) + cos^{2} (45), u = - i - 1 + cos^{2} (60) + cos^{2} (45)

cos^{2} (60) + cos^{2} (45) + u^{2} = 1

cos^{2} (60)

を右側に移動します

cos^{2} (60) + cos^{2} (45) + u^{2} = 1

両辺から

cos^{2} (60)

を引く

cos^{2} (60) + cos^{2} (45) + u^{2} - cos^{2} (60) = 1 - cos^{2} (60)

簡素化

cos^{2} (45) + u^{2} = 1 - cos^{2} (60)

cos^{2} (45) + u^{2} = 1 - cos^{2} (60)

cos^{2} (45)

を右側に移動します

cos^{2} (45) + u^{2} = 1 - cos^{2} (60)

両辺から

cos^{2} (45)

を引く

cos^{2} (45) + u^{2} - cos^{2} (45) = 1 - cos^{2} (60) - cos^{2} (45)

簡素化

u^{2} = 1 - cos^{2} (60) - cos^{2} (45)

u^{2} = 1 - cos^{2} (60) - cos^{2} (45)

x^{2} = f (a)

の場合, 解は

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

u = 1 - cos^{2} (60) - cos^{2} (45), u = - 1 - cos^{2} (60) - cos^{2} (45)

簡素化

1 - cos^{2} (60) - cos^{2} (45) : i - 1 + cos^{2} (60) + cos^{2} (45)

1 - cos^{2} (60) - cos^{2} (45)

虚数の規則を適用する:

- a = i a

= i cos^{2} (60) + cos^{2} (45) - 1

簡素化

- 1 - cos^{2} (60) - cos^{2} (45) : - i - 1 + cos^{2} (60) + cos^{2} (45)

- 1 - cos^{2} (60) - cos^{2} (45)

虚数の規則を適用する:

- a = i a

= - i cos^{2} (60) + cos^{2} (45) - 1

u = i - 1 + cos^{2} (60) + cos^{2} (45), u = - i - 1 + cos^{2} (60) + cos^{2} (45)

代用を戻す

u = cos (x)

cos (x) = i - 1 + cos^{2} (60) + cos^{2} (45), cos (x) = - i - 1 + cos^{2} (60) + cos^{2} (45)

cos (x) = i - 1 + cos^{2} (60) + cos^{2} (45), cos (x) = - i - 1 + cos^{2} (60) + cos^{2} (45)

cos (x) = i - 1 + cos^{2} (60) + cos^{2} (45) :

解なし

cos (x) = i - 1 + cos^{2} (60) + cos^{2} (45)

解なし

cos (x) = - i - 1 + cos^{2} (60) + cos^{2} (45) :

解なし

cos (x) = - i - 1 + cos^{2} (60) + cos^{2} (45)

解なし

すべての解を組み合わせる

以下の解はない : x \in R

グラフ

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