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受欢迎的三角函数 >

4(cot(x)-sqrt(3))=cot(x)-sqrt(3)

解答

4 (cot (x) - 3) = cot (x) - 3

解答

x = \frac{π}{6} + πn

+1

度数

x = 3 0^{\circ} + 18 0^{\circ} n

求解步骤

4 (cot (x) - 3) = cot (x) - 3

用替代法求解

4 (cot (x) - 3) = cot (x) - 3

令

: cot (x) = u

4 (u - 3) = u - 3

4 (u - 3) = u - 3 : u = 3

4 (u - 3) = u - 3

展开

4 (u - 3) : 4 u - 43

4 (u - 3)

使用分配律:

a (b - c) = ab - a c

a = 4, b = u, c = 3

= 4 u - 43

4 u - 43 = u - 3

将

43

到右边

4 u - 43 = u - 3

两边加上

43

4 u - 43 + 43 = u - 3 + 43

化简

4 u - 43 + 43 = u - 3 + 43

化简

4 u - 43 + 43 : 4 u

4 u - 43 + 43

同类项相加:

- 43 + 43 = 0

= 4 u

化简

u - 3 + 43 : u + 33

u - 3 + 43

同类项相加:

- 3 + 43 = 33

= u + 33

4 u = u + 33

4 u = u + 33

4 u = u + 33

将

u

para o lado esquerdo

4 u = u + 33

两边减去

u

4 u - u = u + 33 - u

化简

3 u = 33

3 u = 33

两边除以

3

3 u = 33

两边除以

3

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

化简

u = 3

u = 3

u = cot (x)

代回

cot (x) = 3

cot (x) = 3

cot (x) = 3 : x = \frac{π}{6} + πn

cot (x) = 3

cot (x) = 3

的通解

cot (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} cot (x) \mp \infty 31 \frac{3}{3} 0 - \frac{3}{3} - 1 - 3

x = \frac{π}{6} + πn

x = \frac{π}{6} + πn

合并所有解

x = \frac{π}{6} + πn

作图

流行的例子

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