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受欢迎的三角函数 >

cot(x)cos^2(x)=2cot(x)

解答

cot (x) cos^{2} (x) = 2 cot (x)

解答

x = \frac{π}{2} + πn

+1

度数

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

求解步骤

cot (x) cos^{2} (x) = 2 cot (x)

两边减去

2 cot (x)

cos^{2} (x) cot (x) - 2 cot (x) = 0

分解

cos^{2} (x) cot (x) - 2 cot (x) : cot (x) (cos (x) + 2) (cos (x) - 2)

cos^{2} (x) cot (x) - 2 cot (x)

因式分解出通项

cot (x)

= cot (x) (cos^{2} (x) - 2)

分解

cos^{2} (x) - 2 : (cos (x) + 2) (cos (x) - 2)

cos^{2} (x) - 2

使用根式运算法则:

a = (a)^{2}

2 = (2)^{2}

= cos^{2} (x) - (2)^{2}

使用平方差公式:

x^{2} - y^{2} = (x + y) (x - y)

cos^{2} (x) - (2)^{2} = (cos (x) + 2) (cos (x) - 2)

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

= cot (x) (cos (x) + 2) (cos (x) - 2)

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

分别求解每个部分

cot (x) = 0 or cos (x) + 2 = 0 or cos (x) - 2 = 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

cos (x) + 2 = 0 :

无解

cos (x) + 2 = 0

将

2

到右边

cos (x) + 2 = 0

两边减去

2

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

化简

cos (x) = - 2

cos (x) = - 2

- 1 \leq cos (x) \leq 1

无解

cos (x) - 2 = 0 :

无解

cos (x) - 2 = 0

将

2

到右边

cos (x) - 2 = 0

两边加上

2

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

化简

cos (x) = 2

cos (x) = 2

- 1 \leq cos (x) \leq 1

无解

合并所有解

x = \frac{π}{2} + πn

作图

流行的例子

tan (θ) = 4

sin^2(x)+2cos(x)=2

sin^{2} (x) + 2 cos (x) = 2

cos(4x)=-(sqrt(2))/2

cos (4 x) = - \frac{2}{2}

tan(x)=sqrt(2)sin(x)

tan (x) = 2 sin (x)

cos(2x)+3cos(x)+2=0

cos (2 x) + 3 cos (x) + 2 = 0