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人気のある三角関数 >

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

解

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

解

x = \frac{3 π}{4} + πn, x = \frac{π}{4} + πn

+1

度

x = 13 5^{\circ} + 18 0^{\circ} n, x = 4 5^{\circ} + 18 0^{\circ} n

解答ステップ

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

両辺から

1 - sin^{2} (x)

を引く

sin^{2} (x) tan^{2} (x) - 1 + sin^{2} (x) = 0

三角関数の公式を使用して書き換える

- 1 + sin^{2} (x) + sin^{2} (x) tan^{2} (x)

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

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

簡素化

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

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

拡張

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

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

分配法則を適用する:

a (b - c) = ab - a c

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

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

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

乗算:

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

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

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

簡素化

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

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

条件のようなグループ

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

類似した元を足す:

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

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

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

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

- 1 + sec^{2} (x) sin^{2} (x) = 0

因数

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

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

指数の規則を適用する:

a^{m} b^{m} = (ab)^{m}

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

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

2乗の差の公式を適用する:

x^{2} - y^{2} = (x + y) (x - y)

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

= (sec (x) sin (x) + 1) (sec (x) sin (x) - 1)

(sec (x) sin (x) + 1) (sec (x) sin (x) - 1) = 0

各部分を別個に解く

sec (x) sin (x) + 1 = 0 or sec (x) sin (x) - 1 = 0

sec (x) sin (x) + 1 = 0 : x = \frac{3 π}{4} + πn

sec (x) sin (x) + 1 = 0

三角関数の公式を使用して書き換える

sec (x) sin (x) + 1

sec (x) sin (x) = tan (x)

sec (x) sin (x)

サイン, コサインで表わす

sec (x) sin (x)

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 ( x )} sin (x)

簡素化

\frac{1}{cos ( x )} sin (x) : \frac{sin ( x )}{cos ( x )}

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

分数を乗じる:

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

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

乗算:

1 \cdot sin (x) = sin (x)

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

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

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

基本的な三角関数の公式を使用する:

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

= tan (x)

= 1 + tan (x)

1 + tan (x) = 0

1

を右側に移動します

1 + tan (x) = 0

両辺から

1

を引く

1 + tan (x) - 1 = 0 - 1

簡素化

tan (x) = - 1

tan (x) = - 1

以下の一般解

tan (x) = - 1

tan (x)

πn

循環を含む周期性テーブル:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

x = \frac{3 π}{4} + πn

x = \frac{3 π}{4} + πn

sec (x) sin (x) - 1 = 0 : x = \frac{π}{4} + πn

sec (x) sin (x) - 1 = 0

三角関数の公式を使用して書き換える

sec (x) sin (x) - 1

sec (x) sin (x) = tan (x)

sec (x) sin (x)

サイン, コサインで表わす

sec (x) sin (x)

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 ( x )} sin (x)

簡素化

\frac{1}{cos ( x )} sin (x) : \frac{sin ( x )}{cos ( x )}

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

分数を乗じる:

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

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

乗算:

1 \cdot sin (x) = sin (x)

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

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

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

基本的な三角関数の公式を使用する:

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

= tan (x)

= - 1 + tan (x)

- 1 + tan (x) = 0

1

を右側に移動します

- 1 + tan (x) = 0

両辺に

1

を足す

- 1 + tan (x) + 1 = 0 + 1

簡素化

tan (x) = 1

tan (x) = 1

以下の一般解

tan (x) = 1

tan (x)

πn

循環を含む周期性テーブル:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

x = \frac{π}{4} + πn

x = \frac{π}{4} + πn

すべての解を組み合わせる

x = \frac{3 π}{4} + πn, x = \frac{π}{4} + πn

グラフ

人気の例

2sin^2(x)=3-5cos(x)

2 sin^{2} (x) = 3 - 5 cos (x)

-3cos(2θ)-18sin(θ)-8=-5sin(θ)-6

- 3 cos (2 θ) - 18 sin (θ) - 8 = - 5 sin (θ) - 6

tan^2(x)+4tan(x)=3

tan^{2} (x) + 4 tan (x) = 3

sin (1 - 2 x) = 1

5cos(x)+2=cos(x)

5 cos (x) + 2 = cos (x)