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受欢迎的三角函数 >

3-sqrt(3)tan(2x)=4-2sqrt(3)tan(2x)

解答

3 - 3 tan (2 x) = 4 - 23 tan (2 x)

解答

x = \frac{π}{12} + \frac{πn}{2}

+1

度数

x = 1 5^{\circ} + 9 0^{\circ} n

求解步骤

3 - 3 tan (2 x) = 4 - 23 tan (2 x)

用替代法求解

3 - 3 tan (2 x) = 4 - 23 tan (2 x)

令

: tan (2 x) = u

3 - 3 u = 4 - 23 u

3 - 3 u = 4 - 23 u : u = \frac{3}{3}

3 - 3 u = 4 - 23 u

将

3

到右边

3 - 3 u = 4 - 23 u

两边减去

3

3 - 3 u - 3 = 4 - 23 u - 3

化简

3 - 3 u - 3 = 4 - 23 u - 3

化简

3 - 3 u - 3 : - 3 u

3 - 3 u - 3

同类项相加:

3 - 3 = 0

= - 3 u

化简

4 - 23 u - 3 : - 23 u + 1

4 - 23 u - 3

对同类项分组

= - 23 u + 4 - 3

数字相加/相减:

4 - 3 = 1

= - 23 u + 1

- 3 u = - 23 u + 1

- 3 u = - 23 u + 1

- 3 u = - 23 u + 1

将

23 u

para o lado esquerdo

- 3 u = - 23 u + 1

两边加上

23 u

- 3 u + 23 u = - 23 u + 1 + 23 u

化简

- 3 u + 23 u = - 23 u + 1 + 23 u

化简

- 3 u + 23 u : 3 u

- 3 u + 23 u

同类项相加:

- 3 u + 23 u = 3 u

= 3 u

化简

- 23 u + 1 + 23 u : 1

- 23 u + 1 + 23 u

同类项相加:

- 23 u + 23 u = 0

= 1

3 u = 1

3 u = 1

3 u = 1

两边除以

3

3 u = 1

两边除以

3

\frac{3 u}{3} = \frac{1}{3}

化简

\frac{3 u}{3} = \frac{1}{3}

化简

\frac{3 u}{3} : u

\frac{3 u}{3}

约分:

3

= u

化简

\frac{1}{3} : \frac{3}{3}

\frac{1}{3}

乘以共轭根式

\frac{3}{3}

= \frac{1 \cdot 3}{3 3}

1 \cdot 3 = 3

33 = 3

33

使用根式运算法则:

a a = a

33 = 3

= 3

= \frac{3}{3}

u = \frac{3}{3}

u = \frac{3}{3}

u = \frac{3}{3}

u = tan (2 x)

代回

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

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

tan (2 x) = \frac{3}{3} : x = \frac{π}{12} + \frac{πn}{2}

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

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

的通解

tan (x)

周期表（周期为

πn

）：

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}

2 x = \frac{π}{6} + πn

2 x = \frac{π}{6} + πn

解

2 x = \frac{π}{6} + πn : x = \frac{π}{12} + \frac{πn}{2}

2 x = \frac{π}{6} + πn

两边除以

2

2 x = \frac{π}{6} + πn

两边除以

2

\frac{2 x}{2} = \frac{\frac{π}{6}}{2} + \frac{πn}{2}

化简

\frac{2 x}{2} = \frac{\frac{π}{6}}{2} + \frac{πn}{2}

化简

\frac{2 x}{2} : x

\frac{2 x}{2}

数字相除:

\frac{2}{2} = 1

= x

化简

\frac{\frac{π}{6}}{2} + \frac{πn}{2} : \frac{π}{12} + \frac{πn}{2}

\frac{\frac{π}{6}}{2} + \frac{πn}{2}

\frac{\frac{π}{6}}{2} = \frac{π}{12}

\frac{\frac{π}{6}}{2}

使用分式法则:

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

= \frac{π}{6 \cdot 2}

数字相乘:

6 \cdot 2 = 12

= \frac{π}{12}

= \frac{π}{12} + \frac{πn}{2}

x = \frac{π}{12} + \frac{πn}{2}

x = \frac{π}{12} + \frac{πn}{2}

x = \frac{π}{12} + \frac{πn}{2}

x = \frac{π}{12} + \frac{πn}{2}

合并所有解

x = \frac{π}{12} + \frac{πn}{2}

作图

流行的例子

cos(θ)= 3/(sqrt(34))

cos (θ) = \frac{3}{34}

tan(θ)+cot(θ)= 4/(sqrt(3))

tan (θ) + cot (θ) = \frac{4}{3}

sec(x)+4cos(x)=5

sec (x) + 4 cos (x) = 5

-sqrt(3)sec(x)=2

- 3 sec (x) = 2

3cos(x)csc(x)=2sqrt(3)cos(x)

3 cos (x) csc (x) = 23 cos (x)