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受欢迎的三角函数 >

sec(x)*cot(x)-2cot(x)+sec(x)=2

解答

sec (x) \cdot cot (x) - 2 cot (x) + sec (x) = 2

解答

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn, x = \frac{3 π}{4} + πn

+1

度数

x = 6 0^{\circ} + 36 0^{\circ} n, x = 30 0^{\circ} + 36 0^{\circ} n, x = 13 5^{\circ} + 18 0^{\circ} n

求解步骤

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

两边减去

2

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

分解

sec (x) cot (x) - 2 cot (x) + sec (x) - 2 : (sec (x) - 2) (cot (x) + 1)

sec (x) cot (x) - 2 cot (x) + sec (x) - 2

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

从

cot (x) sec (x) - 2 cot (x)

分解出因式

cot (x)

:

cot (x) (sec (x) - 2)

cot (x) sec (x) - 2 cot (x)

因式分解出通项

cot (x)

= cot (x) (sec (x) - 2)

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

因式分解出通项

sec (x) - 2

= (sec (x) - 2) (cot (x) + 1)

(sec (x) - 2) (cot (x) + 1) = 0

分别求解每个部分

sec (x) - 2 = 0 or cot (x) + 1 = 0

sec (x) - 2 = 0 : x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

sec (x) - 2 = 0

将

2

到右边

sec (x) - 2 = 0

两边加上

2

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

化简

sec (x) = 2

sec (x) = 2

sec (x) = 2

的通解

sec (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} sec (x) 1 \frac{2 3}{3} 22 Undefined - 2 - 2 - \frac{2 3}{3} 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} sec (x) - 1 - \frac{2 3}{3} - 2 - 2 Undefined 22 \frac{2 3}{3}

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

cot (x) + 1 = 0 : x = \frac{3 π}{4} + πn

cot (x) + 1 = 0

将

1

到右边

cot (x) + 1 = 0

两边减去

1

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

化简

cot (x) = - 1

cot (x) = - 1

cot (x) = - 1

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{3 π}{4} + πn

x = \frac{3 π}{4} + πn

合并所有解

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn, x = \frac{3 π}{4} + πn

作图

流行的例子

3sin^2(x)-10sin(x)-8=0

cos(7x)=sin(4x+2)

12cos(β)-5sin(β)=4.7

cos(x)=(sqrt(8))/3

arctan(θ)= 6/8