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受欢迎的三角函数 >

(tan(x)-1)(sec(x)+1)=0

解答

(tan (x) - 1) (sec (x) + 1) = 0

解答

x = \frac{π}{4} + πn, x = π + 2 πn

+1

度数

x = 4 5^{\circ} + 18 0^{\circ} n, x = 18 0^{\circ} + 36 0^{\circ} n

求解步骤

(tan (x) - 1) (sec (x) + 1) = 0

分别求解每个部分

tan (x) - 1 = 0 or sec (x) + 1 = 0

tan (x) - 1 = 0 : x = \frac{π}{4} + πn

tan (x) - 1 = 0

将

1

到右边

tan (x) - 1 = 0

两边加上

1

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

化简

tan (x) = 1

tan (x) = 1

tan (x) = 1

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}

x = \frac{π}{4} + πn

x = \frac{π}{4} + πn

sec (x) + 1 = 0 : x = π + 2 πn

sec (x) + 1 = 0

将

1

到右边

sec (x) + 1 = 0

两边减去

1

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

化简

sec (x) = - 1

sec (x) = - 1

sec (x) = - 1

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 = π + 2 πn

x = π + 2 πn

合并所有解

x = \frac{π}{4} + πn, x = π + 2 πn

作图

流行的例子

tan (θ) = \frac{9}{10}

tan(x)= 3/(sqrt(205))

tan (x) = \frac{3}{205}

sin(x)sin(2x)=sin(3x)

sin (x) sin (2 x) = sin (3 x)

cot (x) = \frac{15}{8}

cos (θ) = \frac{- 5}{4}