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cos(x)tan(x)-tan(x)=0

解答

cos (x) tan (x) - tan (x) = 0

解答

x = πn

+1

度数

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

求解步骤

cos (x) tan (x) - tan (x) = 0

分解

cos (x) tan (x) - tan (x) : tan (x) (cos (x) - 1)

cos (x) tan (x) - tan (x)

因式分解出通项

tan (x)

= tan (x) (cos (x) - 1)

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

分别求解每个部分

tan (x) = 0 or cos (x) - 1 = 0

tan (x) = 0 : x = πn

tan (x) = 0

tan (x) = 0

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 = 0 + πn

x = 0 + πn

解

x = 0 + πn : x = πn

x = 0 + πn

0 + πn = πn

x = πn

x = πn

cos (x) - 1 = 0 : x = 2 πn

cos (x) - 1 = 0

将

1

到右边

cos (x) - 1 = 0

两边加上

1

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

化简

cos (x) = 1

cos (x) = 1

cos (x) = 1

的通解

cos (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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} 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} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

x = 0 + 2 πn

x = 0 + 2 πn

解

x = 0 + 2 πn : x = 2 πn

x = 0 + 2 πn

0 + 2 πn = 2 πn

x = 2 πn

x = 2 πn

合并所有解

x = πn, x = 2 πn

合并重叠的区间

x = πn

流行的例子

sin (x) = - 0.98

2cos^2(x)+9cos(x)=4

2 cos^{2} (x) + 9 cos (x) = 4

sin^2(x)-2=sin(x),-x<= x<= 2pi

sin^{2} (x) - 2 = sin (x), - x \leq x \leq 2 π

sin(2x+60)= 1/2 ,-180<= ,x<= 180

sin (2 x + 60) = \frac{1}{2}, - 18 0^{\circ} \leq, x \leq 18 0^{\circ}

80=arcsin((1.5)/x)

80 = arcsin (\frac{1.5}{x})