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cot(x)-cot(x)csc(x)=0

解答

cot (x) - cot (x) csc (x) = 0

解答

x = \frac{π}{2} + πn

+1

度数

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

求解步骤

cot (x) - cot (x) csc (x) = 0

分解

cot (x) - cot (x) csc (x) : - cot (x) (csc (x) - 1)

cot (x) - cot (x) csc (x)

因式分解出通项

- cot (x)

= - cot (x) (- 1 + csc (x))

- cot (x) (csc (x) - 1) = 0

分别求解每个部分

cot (x) = 0 or csc (x) - 1 = 0

cot (x) = 0 : x = \frac{π}{2} + πn

cot (x) = 0

cot (x) = 0

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}{2} + πn

x = \frac{π}{2} + πn

csc (x) - 1 = 0 : x = \frac{π}{2} + 2 πn

csc (x) - 1 = 0

将

1

到右边

csc (x) - 1 = 0

两边加上

1

csc (x) - 1 + 1 = 0 + 1

化简

csc (x) = 1

csc (x) = 1

csc (x) = 1

的通解

csc (x)

周期表（周期为

2 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} csc (x) Undefiend 22 \frac{2 3}{3} 1 \frac{2 3}{3} 22 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} csc (x) Undefiend - 2 - 2 - \frac{2 3}{3} - 1 - \frac{2 3}{3} - 2 - 2

x = \frac{π}{2} + 2 πn

x = \frac{π}{2} + 2 πn

合并所有解

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

合并重叠的区间

x = \frac{π}{2} + πn

流行的例子

3sin^2(x)-3sin(x)+cos^2(x)=0

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

12cos^2(x)-7cos(x)+1=0

12 cos^{2} (x) - 7 cos (x) + 1 = 0

tan(x/2)tan(x)=-3

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

sin(-x)=-1/3 ,tan(x)=-(sqrt(2))/4

sin (- x) = - \frac{1}{3}, tan (x) = - \frac{2}{4}

solvefor x,h=tan(x-pi/6)求解

x, h = tan (x - \frac{π}{6})