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人気のある三角関数 >

tan(x-20)=tan(2x+10)

解

tan (x - 2 0^{\circ}) = tan (2 x + 10)

解

x = - 36 0^{\circ} n - 2 0^{\circ} - 10, x = - 10 - 20 0^{\circ} - 36 0^{\circ} n

+1

ラジアン

x = - \frac{π}{9} - 10 - 2 πn, x = - 10 - \frac{10 π}{9} - 2 πn

解答ステップ

tan (x - 2 0^{\circ}) = tan (2 x + 10)

両辺から

tan (2 x + 10)

を引く

tan (x - 2 0^{\circ}) - tan (2 x + 10) = 0

サイン, コサインで表わす

tan (- 2 0^{\circ} + x) - tan (10 + 2 x)

基本的な三角関数の公式を使用する:

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

= \frac{sin ( - 2 0 ^{\circ} + x )}{cos ( - 2 0 ^{\circ} + x )} - tan (10 + 2 x)

基本的な三角関数の公式を使用する:

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

= \frac{sin ( - 2 0 ^{\circ} + x )}{cos ( - 2 0 ^{\circ} + x )} - \frac{sin ( 10 + 2 x )}{cos ( 10 + 2 x )}

簡素化

\frac{sin ( - 2 0 ^{\circ} + x )}{cos ( - 2 0 ^{\circ} + x )} - \frac{sin ( 10 + 2 x )}{cos ( 10 + 2 x )} : \frac{sin ( \frac{- 18 0 ^{\circ} + 9 x}{9} ) cos ( 2 x + 10 ) - sin ( 10 + 2 x ) cos ( \frac{9 x - 18 0 ^{\circ}}{9} )}{cos ( \frac{9 x - 18 0 ^{\circ}}{9} ) cos ( 2 x + 10 )}

\frac{sin ( - 2 0 ^{\circ} + x )}{cos ( - 2 0 ^{\circ} + x )} - \frac{sin ( 10 + 2 x )}{cos ( 10 + 2 x )}

\frac{sin ( - 2 0 ^{\circ} + x )}{cos ( - 2 0 ^{\circ} + x )} = \frac{sin ( \frac{- 18 0 ^{\circ} + 9 x}{9} )}{cos ( \frac{- 18 0 ^{\circ} + 9 x}{9} )}

\frac{sin ( - 2 0 ^{\circ} + x )}{cos ( - 2 0 ^{\circ} + x )}

結合

- 2 0^{\circ} + x : \frac{- 18 0 ^{\circ} + 9 x}{9}

- 2 0^{\circ} + x

元を分数に変換する:

x = \frac{x 9}{9}

= - 2 0^{\circ} + \frac{x \cdot 9}{9}

分母が等しいので, 分数を組み合わせる:

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

= \frac{- 18 0 ^{\circ} + x \cdot 9}{9}

= \frac{sin ( - 2 0 ^{\circ} + x )}{cos ( \frac{- 18 0 ^{\circ} + x \cdot 9}{9} )}

結合

- 2 0^{\circ} + x : \frac{- 18 0 ^{\circ} + 9 x}{9}

- 2 0^{\circ} + x

元を分数に変換する:

x = \frac{x 9}{9}

= - 2 0^{\circ} + \frac{x \cdot 9}{9}

分母が等しいので, 分数を組み合わせる:

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

= \frac{- 18 0 ^{\circ} + x \cdot 9}{9}

= \frac{sin ( \frac{- 18 0 ^{\circ} + x \cdot 9}{9} )}{cos ( \frac{- 18 0 ^{\circ} + x \cdot 9}{9} )}

= \frac{sin ( \frac{9 x - 18 0 ^{\circ}}{9} )}{cos ( \frac{9 x - 18 0 ^{\circ}}{9} )} - \frac{sin ( 2 x + 10 )}{cos ( 2 x + 10 )}

以下の最小公倍数:

cos (\frac{- 18 0 ^{\circ} + x 9}{9}), cos (10 + 2 x) : cos (\frac{9 x - 18 0 ^{\circ}}{9}) cos (2 x + 10)

cos (\frac{- 18 0 ^{\circ} + x \cdot 9}{9}), cos (10 + 2 x)

最小公倍数 (LCM)

cos (\frac{- 18 0 ^{\circ} + x 9}{9})

または以下のいずれかに現れる因数で構成された式を計算する:

cos (10 + 2 x)

= cos (\frac{9 x - 18 0 ^{\circ}}{9}) cos (2 x + 10)

LCMに基づいて分数を調整する

該当する分母を乗じてLCMに変えるために

必要な量で各分子を乗じる

cos (\frac{9 x - 18 0 ^{\circ}}{9}) cos (2 x + 10)

\frac{sin ( \frac{- 18 0 ^{\circ} + x \cdot 9}{9} )}{cos ( \frac{- 18 0 ^{\circ} + x \cdot 9}{9} )}

の場合

:

分母と分子に以下を乗じる:

cos (2 x + 10)

\frac{sin ( \frac{- 18 0 ^{\circ} + x \cdot 9}{9} )}{cos ( \frac{- 18 0 ^{\circ} + x \cdot 9}{9} )} = \frac{sin ( \frac{- 18 0 ^{\circ} + x \cdot 9}{9} ) cos ( 2 x + 10 )}{cos ( \frac{- 18 0 ^{\circ} + x \cdot 9}{9} ) cos ( 2 x + 10 )}

\frac{sin ( 10 + 2 x )}{cos ( 10 + 2 x )}

の場合

:

分母と分子に以下を乗じる:

cos (\frac{9 x - 18 0 ^{\circ}}{9})

\frac{sin ( 10 + 2 x )}{cos ( 10 + 2 x )} = \frac{sin ( 10 + 2 x ) cos ( \frac{9 x - 18 0 ^{\circ}}{9} )}{cos ( 10 + 2 x ) cos ( \frac{9 x - 18 0 ^{\circ}}{9} )}

= \frac{sin ( \frac{- 18 0 ^{\circ} + x \cdot 9}{9} ) cos ( 2 x + 10 )}{cos ( \frac{- 18 0 ^{\circ} + x \cdot 9}{9} ) cos ( 2 x + 10 )} - \frac{sin ( 10 + 2 x ) cos ( \frac{9 x - 18 0 ^{\circ}}{9} )}{cos ( 10 + 2 x ) cos ( \frac{9 x - 18 0 ^{\circ}}{9} )}

分母が等しいので, 分数を組み合わせる:

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

= \frac{sin ( \frac{- 18 0 ^{\circ} + x \cdot 9}{9} ) cos ( 2 x + 10 ) - sin ( 10 + 2 x ) cos ( \frac{9 x - 18 0 ^{\circ}}{9} )}{cos ( \frac{9 x - 18 0 ^{\circ}}{9} ) cos ( 2 x + 10 )}

= \frac{sin ( \frac{- 18 0 ^{\circ} + 9 x}{9} ) cos ( 2 x + 10 ) - sin ( 10 + 2 x ) cos ( \frac{9 x - 18 0 ^{\circ}}{9} )}{cos ( \frac{9 x - 18 0 ^{\circ}}{9} ) cos ( 2 x + 10 )}

\frac{cos ( 10 + 2 x ) sin ( \frac{- 18 0 ^{\circ} + 9 x}{9} ) - cos ( \frac{- 18 0 ^{\circ} + 9 x}{9} ) sin ( 10 + 2 x )}{cos ( 10 + 2 x ) cos ( \frac{- 18 0 ^{\circ} + 9 x}{9} )} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

cos (10 + 2 x) sin (\frac{- 18 0 ^{\circ} + 9 x}{9}) - cos (\frac{- 18 0 ^{\circ} + 9 x}{9}) sin (10 + 2 x) = 0

三角関数の公式を使用して書き換える

cos (10 + 2 x) sin (\frac{- 18 0 ^{\circ} + 9 x}{9}) - cos (\frac{- 18 0 ^{\circ} + 9 x}{9}) sin (10 + 2 x)

角の差の公式を使用する:

sin (s) cos (t) - cos (s) sin (t) = sin (s - t)

= sin (\frac{- 18 0 ^{\circ} + 9 x}{9} - (10 + 2 x))

sin (\frac{- 18 0 ^{\circ} + 9 x}{9} - (10 + 2 x)) = 0

以下の一般解

sin (\frac{- 18 0 ^{\circ} + 9 x}{9} - (10 + 2 x)) = 0

sin (x)

36 0^{\circ} n

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} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

\frac{- 18 0 ^{\circ} + 9 x}{9} - (10 + 2 x) = 0 + 36 0^{\circ} n, \frac{- 18 0 ^{\circ} + 9 x}{9} - (10 + 2 x) = 18 0^{\circ} + 36 0^{\circ} n

\frac{- 18 0 ^{\circ} + 9 x}{9} - (10 + 2 x) = 0 + 36 0^{\circ} n, \frac{- 18 0 ^{\circ} + 9 x}{9} - (10 + 2 x) = 18 0^{\circ} + 36 0^{\circ} n

解く

\frac{- 18 0 ^{\circ} + 9 x}{9} - (10 + 2 x) = 0 + 36 0^{\circ} n : x = - 36 0^{\circ} n - 2 0^{\circ} - 10

\frac{- 18 0 ^{\circ} + 9 x}{9} - (10 + 2 x) = 0 + 36 0^{\circ} n

0 + 36 0^{\circ} n = 36 0^{\circ} n

\frac{- 18 0 ^{\circ} + 9 x}{9} - (10 + 2 x) = 36 0^{\circ} n

以下で両辺を乗じる:

9

\frac{- 18 0 ^{\circ} + 9 x}{9} - (10 + 2 x) = 36 0^{\circ} n

以下で両辺を乗じる:

9

\frac{- 18 0 ^{\circ} + 9 x}{9} \cdot 9 - (10 + 2 x) \cdot 9 = 36 0^{\circ} n \cdot 9

簡素化

\frac{- 18 0 ^{\circ} + 9 x}{9} \cdot 9 - (10 + 2 x) \cdot 9 = 36 0^{\circ} n \cdot 9

簡素化

\frac{- 18 0 ^{\circ} + 9 x}{9} \cdot 9 : - 18 0^{\circ} + 9 x

\frac{- 18 0 ^{\circ} + 9 x}{9} \cdot 9

分数を乗じる:

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

= \frac{( - 18 0 ^{\circ} + 9 x ) \cdot 9}{9}

共通因数を約分する:

9

= - - 18 0^{\circ} + 9 x

簡素化

(10 + 2 x) \cdot 9 : 9 (10 + 2 x)

(10 + 2 x) \cdot 9

交換法則を適用する:

(10 + 2 x) \cdot 9 = 9 (10 + 2 x)

9 (10 + 2 x)

簡素化

36 0^{\circ} n \cdot 9 : 324 0^{\circ} n

36 0^{\circ} n \cdot 9

数を乗じる:

2 \cdot 9 = 18

= 324 0^{\circ} n

- 18 0^{\circ} + 9 x - 9 (10 + 2 x) = 324 0^{\circ} n

- 18 0^{\circ} + 9 x - 9 (10 + 2 x) = 324 0^{\circ} n

- 18 0^{\circ} + 9 x - 9 (10 + 2 x) = 324 0^{\circ} n

拡張

- 18 0^{\circ} + 9 x - 9 (10 + 2 x) : - 9 x - 18 0^{\circ} - 90

- 18 0^{\circ} + 9 x - 9 (10 + 2 x)

拡張

- 9 (10 + 2 x) : - 90 - 18 x

- 9 (10 + 2 x)

分配法則を適用する:

a (b + c) = ab + a c

a = - 9, b = 10, c = 2 x

= - 9 \cdot 10 + (- 9) \cdot 2 x

マイナス・プラスの規則を適用する

+ (- a) = - a

= - 9 \cdot 10 - 9 \cdot 2 x

簡素化

- 9 \cdot 10 - 9 \cdot 2 x : - 90 - 18 x

- 9 \cdot 10 - 9 \cdot 2 x

数を乗じる:

9 \cdot 10 = 90

= - 90 - 9 \cdot 2 x

数を乗じる:

9 \cdot 2 = 18

= - 90 - 18 x

= - 90 - 18 x

= - 18 0^{\circ} + 9 x - 90 - 18 x

簡素化

- 18 0^{\circ} + 9 x - 90 - 18 x : - 9 x - 18 0^{\circ} - 90

- 18 0^{\circ} + 9 x - 90 - 18 x

条件のようなグループ

= 9 x - 18 x - 18 0^{\circ} - 90

類似した元を足す:

9 x - 18 x = - 9 x

= - 9 x - 18 0^{\circ} - 90

= - 9 x - 18 0^{\circ} - 90

- 9 x - 18 0^{\circ} - 90 = 324 0^{\circ} n

18 0^{\circ}

を右側に移動します

- 9 x - 18 0^{\circ} - 90 = 324 0^{\circ} n

両辺に

18 0^{\circ}

を足す

- 9 x - 18 0^{\circ} - 90 + 18 0^{\circ} = 324 0^{\circ} n + 18 0^{\circ}

簡素化

- 9 x - 90 = 324 0^{\circ} n + 18 0^{\circ}

- 9 x - 90 = 324 0^{\circ} n + 18 0^{\circ}

90

を右側に移動します

- 9 x - 90 = 324 0^{\circ} n + 18 0^{\circ}

両辺に

90

を足す

- 9 x - 90 + 90 = 324 0^{\circ} n + 18 0^{\circ} + 90

簡素化

- 9 x = 324 0^{\circ} n + 18 0^{\circ} + 90

- 9 x = 324 0^{\circ} n + 18 0^{\circ} + 90

以下で両辺を割る

- 9

- 9 x = 324 0^{\circ} n + 18 0^{\circ} + 90

以下で両辺を割る

- 9

\frac{- 9 x}{- 9} = \frac{324 0 ^{\circ} n}{- 9} + \frac{18 0 ^{\circ}}{- 9} + \frac{90}{- 9}

簡素化

\frac{- 9 x}{- 9} = \frac{324 0 ^{\circ} n}{- 9} + \frac{18 0 ^{\circ}}{- 9} + \frac{90}{- 9}

簡素化

\frac{- 9 x}{- 9} : x

\frac{- 9 x}{- 9}

分数の規則を適用する:

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

= \frac{9 x}{9}

数を割る:

\frac{9}{9} = 1

= x

簡素化

\frac{324 0 ^{\circ} n}{- 9} + \frac{18 0 ^{\circ}}{- 9} + \frac{90}{- 9} : - 36 0^{\circ} n - 2 0^{\circ} - 10

\frac{324 0 ^{\circ} n}{- 9} + \frac{18 0 ^{\circ}}{- 9} + \frac{90}{- 9}

\frac{324 0 ^{\circ} n}{- 9} = - 36 0^{\circ} n

\frac{324 0 ^{\circ} n}{- 9}

分数の規則を適用する:

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

= - \frac{324 0 ^{\circ} n}{9}

数を割る:

\frac{18}{9} = 2

= - 36 0^{\circ} n

= - 36 0^{\circ} n + \frac{18 0 ^{\circ}}{- 9} + \frac{90}{- 9}

分数の規則を適用する:

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

= - 36 0^{\circ} n - 2 0^{\circ} + \frac{90}{- 9}

\frac{90}{- 9} = - 10

\frac{90}{- 9}

分数の規則を適用する:

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

= - \frac{90}{9}

数を割る:

\frac{90}{9} = 10

= - 10

= - 36 0^{\circ} n - 2 0^{\circ} - 10

x = - 36 0^{\circ} n - 2 0^{\circ} - 10

x = - 36 0^{\circ} n - 2 0^{\circ} - 10

x = - 36 0^{\circ} n - 2 0^{\circ} - 10

解く

\frac{- 18 0 ^{\circ} + 9 x}{9} - (10 + 2 x) = 18 0^{\circ} + 36 0^{\circ} n : x = - 10 - 20 0^{\circ} - 36 0^{\circ} n

\frac{- 18 0 ^{\circ} + 9 x}{9} - (10 + 2 x) = 18 0^{\circ} + 36 0^{\circ} n

以下で両辺を乗じる:

9

\frac{- 18 0 ^{\circ} + 9 x}{9} - (10 + 2 x) = 18 0^{\circ} + 36 0^{\circ} n

以下で両辺を乗じる:

9

\frac{- 18 0 ^{\circ} + 9 x}{9} \cdot 9 - (10 + 2 x) \cdot 9 = 18 0^{\circ} 9 + 36 0^{\circ} n \cdot 9

簡素化

\frac{- 18 0 ^{\circ} + 9 x}{9} \cdot 9 - (10 + 2 x) \cdot 9 = 18 0^{\circ} 9 + 36 0^{\circ} n \cdot 9

簡素化

\frac{- 18 0 ^{\circ} + 9 x}{9} \cdot 9 : - 18 0^{\circ} + 9 x

\frac{- 18 0 ^{\circ} + 9 x}{9} \cdot 9

分数を乗じる:

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

= \frac{( - 18 0 ^{\circ} + 9 x ) \cdot 9}{9}

共通因数を約分する:

9

= - - 18 0^{\circ} + 9 x

簡素化

(10 + 2 x) \cdot 9 : 9 (10 + 2 x)

(10 + 2 x) \cdot 9

交換法則を適用する:

(10 + 2 x) \cdot 9 = 9 (10 + 2 x)

9 (10 + 2 x)

簡素化

18 0^{\circ} 9 : 162 0^{\circ}

18 0^{\circ} 9

交換法則を適用する:

18 0^{\circ} 9 = 162 0^{\circ}

162 0^{\circ}

簡素化

36 0^{\circ} n \cdot 9 : 324 0^{\circ} n

36 0^{\circ} n \cdot 9

数を乗じる:

2 \cdot 9 = 18

= 324 0^{\circ} n

- 18 0^{\circ} + 9 x - 9 (10 + 2 x) = 162 0^{\circ} + 324 0^{\circ} n

- 18 0^{\circ} + 9 x - 9 (10 + 2 x) = 162 0^{\circ} + 324 0^{\circ} n

- 18 0^{\circ} + 9 x - 9 (10 + 2 x) = 162 0^{\circ} + 324 0^{\circ} n

拡張

- 18 0^{\circ} + 9 x - 9 (10 + 2 x) : - 9 x - 18 0^{\circ} - 90

- 18 0^{\circ} + 9 x - 9 (10 + 2 x)

拡張

- 9 (10 + 2 x) : - 90 - 18 x

- 9 (10 + 2 x)

分配法則を適用する:

a (b + c) = ab + a c

a = - 9, b = 10, c = 2 x

= - 9 \cdot 10 + (- 9) \cdot 2 x

マイナス・プラスの規則を適用する

+ (- a) = - a

= - 9 \cdot 10 - 9 \cdot 2 x

簡素化

- 9 \cdot 10 - 9 \cdot 2 x : - 90 - 18 x

- 9 \cdot 10 - 9 \cdot 2 x

数を乗じる:

9 \cdot 10 = 90

= - 90 - 9 \cdot 2 x

数を乗じる:

9 \cdot 2 = 18

= - 90 - 18 x

= - 90 - 18 x

= - 18 0^{\circ} + 9 x - 90 - 18 x

簡素化

- 18 0^{\circ} + 9 x - 90 - 18 x : - 9 x - 18 0^{\circ} - 90

- 18 0^{\circ} + 9 x - 90 - 18 x

条件のようなグループ

= 9 x - 18 x - 18 0^{\circ} - 90

類似した元を足す:

9 x - 18 x = - 9 x

= - 9 x - 18 0^{\circ} - 90

= - 9 x - 18 0^{\circ} - 90

- 9 x - 18 0^{\circ} - 90 = 162 0^{\circ} + 324 0^{\circ} n

18 0^{\circ}

を右側に移動します

- 9 x - 18 0^{\circ} - 90 = 162 0^{\circ} + 324 0^{\circ} n

両辺に

18 0^{\circ}

を足す

- 9 x - 18 0^{\circ} - 90 + 18 0^{\circ} = 162 0^{\circ} + 324 0^{\circ} n + 18 0^{\circ}

簡素化

- 9 x - 90 = 180 0^{\circ} + 324 0^{\circ} n

- 9 x - 90 = 180 0^{\circ} + 324 0^{\circ} n

90

を右側に移動します

- 9 x - 90 = 180 0^{\circ} + 324 0^{\circ} n

両辺に

90

を足す

- 9 x - 90 + 90 = 180 0^{\circ} + 324 0^{\circ} n + 90

簡素化

- 9 x = 180 0^{\circ} + 324 0^{\circ} n + 90

- 9 x = 180 0^{\circ} + 324 0^{\circ} n + 90

以下で両辺を割る

- 9

- 9 x = 180 0^{\circ} + 324 0^{\circ} n + 90

以下で両辺を割る

- 9

\frac{- 9 x}{- 9} = \frac{180 0 ^{\circ}}{- 9} + \frac{324 0 ^{\circ} n}{- 9} + \frac{90}{- 9}

簡素化

\frac{- 9 x}{- 9} = \frac{180 0 ^{\circ}}{- 9} + \frac{324 0 ^{\circ} n}{- 9} + \frac{90}{- 9}

簡素化

\frac{- 9 x}{- 9} : x

\frac{- 9 x}{- 9}

分数の規則を適用する:

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

= \frac{9 x}{9}

数を割る:

\frac{9}{9} = 1

= x

簡素化

\frac{180 0 ^{\circ}}{- 9} + \frac{324 0 ^{\circ} n}{- 9} + \frac{90}{- 9} : - 10 - 20 0^{\circ} - 36 0^{\circ} n

\frac{180 0 ^{\circ}}{- 9} + \frac{324 0 ^{\circ} n}{- 9} + \frac{90}{- 9}

条件のようなグループ

= \frac{90}{- 9} + \frac{180 0 ^{\circ}}{- 9} + \frac{324 0 ^{\circ} n}{- 9}

\frac{90}{- 9} = - 10

\frac{90}{- 9}

分数の規則を適用する:

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

= - \frac{90}{9}

数を割る:

\frac{90}{9} = 10

= - 10

= - 10 + \frac{180 0 ^{\circ}}{- 9} + \frac{324 0 ^{\circ} n}{- 9}

分数の規則を適用する:

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

= - 10 - 20 0^{\circ} + \frac{324 0 ^{\circ} n}{- 9}

\frac{324 0 ^{\circ} n}{- 9} = - 36 0^{\circ} n

\frac{324 0 ^{\circ} n}{- 9}

分数の規則を適用する:

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

= - \frac{324 0 ^{\circ} n}{9}

数を割る:

\frac{18}{9} = 2

= - 36 0^{\circ} n

= - 10 - 20 0^{\circ} - 36 0^{\circ} n

x = - 10 - 20 0^{\circ} - 36 0^{\circ} n

x = - 10 - 20 0^{\circ} - 36 0^{\circ} n

x = - 10 - 20 0^{\circ} - 36 0^{\circ} n

x = - 36 0^{\circ} n - 2 0^{\circ} - 10, x = - 10 - 20 0^{\circ} - 36 0^{\circ} n

グラフ

人気の例

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sin (5 x) cos (x) - cos (5 x) sin (x) = 0

2 sin (3 x + 1) + 1 = 2

2 sin (3 x + 1) + 1 = 1

sin (x) = 6946

sin(2x)-(sqrt(3))/2 =0,-2pi<= x<= 2pi

sin (2 x) - \frac{3}{2} = 0, - 2 π \leq x \leq 2 π