zs

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

受欢迎的三角函数 >

cos(45+x)-cos(45-x)=sqrt(2)cos(x)

解答

cos (4 5^{\circ} + x) - cos (4 5^{\circ} - x) = 2 cos (x)

解答

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

+1

弧度

x = \frac{3 π}{4} + πn

求解步骤

cos (4 5^{\circ} + x) - cos (4 5^{\circ} - x) = 2 cos (x)

使用三角恒等式改写

cos (4 5^{\circ} + x) - cos (4 5^{\circ} - x) = 2 cos (x)

使用三角恒等式改写

cos (4 5^{\circ} - x)

使用角差恒等式:

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

= cos (4 5^{\circ}) cos (x) + sin (4 5^{\circ}) sin (x)

化简

cos (4 5^{\circ}) cos (x) + sin (4 5^{\circ}) sin (x) : \frac{2 cos ( x ) + 2 sin ( x )}{2}

cos (4 5^{\circ}) cos (x) + sin (4 5^{\circ}) sin (x)

cos (4 5^{\circ}) cos (x) = \frac{2 cos ( x )}{2}

cos (4 5^{\circ}) cos (x)

化简

cos (4 5^{\circ}) : \frac{2}{2}

cos (4 5^{\circ})

使用以下普通恒等式:

cos (4 5^{\circ}) = \frac{2}{2}

cos (x)

周期表（周期为

36 0^{\circ} n

）：

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= \frac{2}{2}

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

分式相乘:

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

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

sin (4 5^{\circ}) sin (x) = \frac{2 sin ( x )}{2}

sin (4 5^{\circ}) sin (x)

化简

sin (4 5^{\circ}) : \frac{2}{2}

sin (4 5^{\circ})

使用以下普通恒等式:

sin (4 5^{\circ}) = \frac{2}{2}

sin (x)

周期表（周期为

36 0^{\circ} n

"）：

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{2}{2}

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

分式相乘:

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

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

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

使用法则

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

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

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

使用角和恒等式:

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

= cos (4 5^{\circ}) cos (x) - sin (4 5^{\circ}) sin (x)

化简

cos (4 5^{\circ}) cos (x) - sin (4 5^{\circ}) sin (x) : \frac{2 cos ( x ) - 2 sin ( x )}{2}

cos (4 5^{\circ}) cos (x) - sin (4 5^{\circ}) sin (x)

cos (4 5^{\circ}) cos (x) = \frac{2 cos ( x )}{2}

cos (4 5^{\circ}) cos (x)

化简

cos (4 5^{\circ}) : \frac{2}{2}

cos (4 5^{\circ})

使用以下普通恒等式:

cos (4 5^{\circ}) = \frac{2}{2}

cos (x)

周期表（周期为

36 0^{\circ} n

）：

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= \frac{2}{2}

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

分式相乘:

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

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

sin (4 5^{\circ}) sin (x) = \frac{2 sin ( x )}{2}

sin (4 5^{\circ}) sin (x)

化简

sin (4 5^{\circ}) : \frac{2}{2}

sin (4 5^{\circ})

使用以下普通恒等式:

sin (4 5^{\circ}) = \frac{2}{2}

sin (x)

周期表（周期为

36 0^{\circ} n

"）：

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{2}{2}

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

分式相乘:

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

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

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

使用法则

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

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

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

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

化简

\frac{2 cos ( x ) - 2 sin ( x )}{2} - \frac{2 cos ( x ) + 2 sin ( x )}{2} : - 2 sin (x)

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

使用法则

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

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

乘开

2 cos (x) - 2 sin (x) - (2 cos (x) + 2 sin (x)) : - 22 sin (x)

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

- (2 cos (x) + 2 sin (x)) : - 2 cos (x) - 2 sin (x)

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

打开括号

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

使用加减运算法则

+ (- a) = - a

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

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

化简

2 cos (x) - 2 sin (x) - 2 cos (x) - 2 sin (x) : - 22 sin (x)

2 cos (x) - 2 sin (x) - 2 cos (x) - 2 sin (x)

同类项相加:

2 cos (x) - 2 cos (x) = 0

= - 2 sin (x) - 2 sin (x)

同类项相加:

- 2 sin (x) - 2 sin (x) = - 22 sin (x)

= - 22 sin (x)

= - 22 sin (x)

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

使用分式法则:

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

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

数字相除:

\frac{2}{2} = 1

= - 2 sin (x)

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

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

两边减去

2 cos (x)

- 2 sin (x) - 2 cos (x) = 0

使用三角恒等式改写

- 2 sin (x) - 2 cos (x) = 0

在两边除以

cos (x), cos (x) \neq = 0

\frac{- 2 sin ( x ) - 2 cos ( x )}{cos ( x )} = \frac{0}{cos ( x )}

化简

- \frac{2 sin ( x )}{cos ( x )} - 2 = 0

使用基本三角恒等式:

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

- 2 tan (x) - 2 = 0

- 2 tan (x) - 2 = 0

将

2

到右边

- 2 tan (x) - 2 = 0

两边加上

2

- 2 tan (x) - 2 + 2 = 0 + 2

化简

- 2 tan (x) = 2

- 2 tan (x) = 2

两边除以

- 2

- 2 tan (x) = 2

两边除以

- 2

\frac{- 2 tan ( x )}{- 2} = \frac{2}{- 2}

化简

tan (x) = - 1

tan (x) = - 1

tan (x) = - 1

的通解

tan (x)

周期表（周期为

18 0^{\circ} n

）：

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

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

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

作图

流行的例子

sin(b)=cos(2b-30)

sin (b) = cos (2 b - 30)

2sin(x)cos(x)-4cos(x)-sin(x)+2=0

2 sin (x) cos (x) - 4 cos (x) - sin (x) + 2 = 0

(sin(pi/2))/5 =(sin(x))/4

\frac{sin ( \frac{π}{2} )}{5} = \frac{sin ( x )}{4}

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

sin(b)=(sqrt(2))/2

sin (b) = \frac{2}{2}