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人気のある三角関数 >

1+cos^2(a)=3sin(x)cos(x)

解

1 + cos^{2} (a) = 3 sin (x) cos (x)

解

x = \frac{arcsin ( - \frac{- 2 c o s ^{2} ( a ) - 2}{3} )}{2} + πn, x = \frac{π}{2} + \frac{arcsin ( \frac{- 2 c o s ^{2} ( a ) - 2}{3} )}{2} + πn

解答ステップ

1 + cos^{2} (a) = 3 sin (x) cos (x)

両辺から

3 sin (x) cos (x)

を引く

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

三角関数の公式を使用して書き換える

1 + cos^{2} (a) - 3 sin (x) cos (x)

2倍角の公式を使用:

2 sin (x) cos (x) = sin (2 x)

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

= 1 + cos^{2} (a) - 3 \cdot \frac{sin ( 2 x )}{2}

1 + cos^{2} (a) - 3 \cdot \frac{sin ( 2 x )}{2} = 0

cos^{2} (a)

を右側に移動します

1 + cos^{2} (a) - 3 \cdot \frac{sin ( 2 x )}{2} = 0

両辺から

cos^{2} (a)

を引く

1 + cos^{2} (a) - 3 \cdot \frac{sin ( 2 x )}{2} - cos^{2} (a) = 0 - cos^{2} (a)

簡素化

1 - 3 \cdot \frac{sin ( 2 x )}{2} = - cos^{2} (a)

1 - 3 \cdot \frac{sin ( 2 x )}{2} = - cos^{2} (a)

1

を右側に移動します

1 - 3 \cdot \frac{sin ( 2 x )}{2} = - cos^{2} (a)

両辺から

1

を引く

1 - 3 \cdot \frac{sin ( 2 x )}{2} - 1 = - cos^{2} (a) - 1

簡素化

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

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

改良

- 3 \cdot \frac{sin ( 2 x )}{2} : - \frac{3 sin ( 2 x )}{2}

- 3 \cdot \frac{sin ( 2 x )}{2}

分数を乗じる:

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

= - \frac{sin ( 2 x ) \cdot 3}{2}

- \frac{3 sin ( 2 x )}{2} = - cos^{2} (a) - 1

以下で両辺を乗じる:

2

- \frac{3 sin ( 2 x )}{2} = - cos^{2} (a) - 1

以下で両辺を乗じる:

2

- \frac{3 sin ( 2 x )}{2} \cdot 2 = - cos^{2} (a) \cdot 2 - 1 \cdot 2

簡素化

- \frac{3 sin ( 2 x )}{2} \cdot 2 = - cos^{2} (a) \cdot 2 - 1 \cdot 2

簡素化

- \frac{3 sin ( 2 x )}{2} \cdot 2 : - 3 sin (2 x)

- \frac{3 sin ( 2 x )}{2} \cdot 2

分数を乗じる:

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

= - \frac{3 sin ( 2 x ) \cdot 2}{2}

共通因数を約分する:

2

= - 3 sin (2 x)

簡素化

cos^{2} (a) \cdot 2 : 2 cos^{2} (a)

cos^{2} (a) \cdot 2

交換法則を適用する:

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

2 cos^{2} (a)

簡素化

- 1 \cdot 2 : - 2

- 1 \cdot 2

数を乗じる:

1 \cdot 2 = 2

= - 2

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

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

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

以下で両辺を割る

- 3

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

以下で両辺を割る

- 3

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

簡素化

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

簡素化

\frac{- 3 sin ( 2 x )}{- 3} : sin (2 x)

\frac{- 3 sin ( 2 x )}{- 3}

分数の規則を適用する:

\frac{- a}{- b} = \frac{a}{b}

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

数を割る:

\frac{3}{3} = 1

= sin (2 x)

簡素化

- \frac{2 cos ^{2} ( a )}{- 3} - \frac{2}{- 3} : - \frac{- 2 cos ^{2} ( a ) - 2}{3}

- \frac{2 cos ^{2} ( a )}{- 3} - \frac{2}{- 3}

規則を適用

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

= \frac{- 2 cos ^{2} ( a ) - 2}{- 3}

分数の規則を適用する:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{- 2 cos ^{2} ( a ) - 2}{3}

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

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

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

三角関数の逆数プロパティを適用する

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

以下の一般解

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

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π + arcsin (a) + 2 πn

2 x = arcsin (- \frac{- 2 cos ^{2} ( a ) - 2}{3}) + 2 πn, 2 x = π + arcsin (\frac{- 2 cos ^{2} ( a ) - 2}{3}) + 2 πn

2 x = arcsin (- \frac{- 2 cos ^{2} ( a ) - 2}{3}) + 2 πn, 2 x = π + arcsin (\frac{- 2 cos ^{2} ( a ) - 2}{3}) + 2 πn

解く

2 x = arcsin (- \frac{- 2 cos ^{2} ( a ) - 2}{3}) + 2 πn : x = \frac{arcsin ( - \frac{- 2 c o s ^{2} ( a ) - 2}{3} )}{2} + πn

2 x = arcsin (- \frac{- 2 cos ^{2} ( a ) - 2}{3}) + 2 πn

以下で両辺を割る

2

2 x = arcsin (- \frac{- 2 cos ^{2} ( a ) - 2}{3}) + 2 πn

以下で両辺を割る

2

\frac{2 x}{2} = \frac{arcsin ( - \frac{- 2 c o s ^{2} ( a ) - 2}{3} )}{2} + \frac{2 πn}{2}

簡素化

x = \frac{arcsin ( - \frac{- 2 c o s ^{2} ( a ) - 2}{3} )}{2} + πn

x = \frac{arcsin ( - \frac{- 2 c o s ^{2} ( a ) - 2}{3} )}{2} + πn

解く

2 x = π + arcsin (\frac{- 2 cos ^{2} ( a ) - 2}{3}) + 2 πn : x = \frac{π}{2} + \frac{arcsin ( \frac{- 2 c o s ^{2} ( a ) - 2}{3} )}{2} + πn

2 x = π + arcsin (\frac{- 2 cos ^{2} ( a ) - 2}{3}) + 2 πn

以下で両辺を割る

2

2 x = π + arcsin (\frac{- 2 cos ^{2} ( a ) - 2}{3}) + 2 πn

以下で両辺を割る

2

\frac{2 x}{2} = \frac{π}{2} + \frac{arcsin ( \frac{- 2 c o s ^{2} ( a ) - 2}{3} )}{2} + \frac{2 πn}{2}

簡素化

x = \frac{π}{2} + \frac{arcsin ( \frac{- 2 c o s ^{2} ( a ) - 2}{3} )}{2} + πn

x = \frac{π}{2} + \frac{arcsin ( \frac{- 2 c o s ^{2} ( a ) - 2}{3} )}{2} + πn

x = \frac{arcsin ( - \frac{- 2 c o s ^{2} ( a ) - 2}{3} )}{2} + πn, x = \frac{π}{2} + \frac{arcsin ( \frac{- 2 c o s ^{2} ( a ) - 2}{3} )}{2} + πn

グラフ

人気の例

3cos(x)+sin(x)=cos(x)-2sin(x)

2cos(x)=cos^2(x)

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

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