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受欢迎的三角函数 >

tan(x)sin^2(x)=2tan(x)

解答

tan (x) sin^{2} (x) = 2 tan (x)

解答

x = πn

+1

度数

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

求解步骤

tan (x) sin^{2} (x) = 2 tan (x)

两边减去

2 tan (x)

sin^{2} (x) tan (x) - 2 tan (x) = 0

分解

sin^{2} (x) tan (x) - 2 tan (x) : tan (x) (sin (x) + 2) (sin (x) - 2)

sin^{2} (x) tan (x) - 2 tan (x)

因式分解出通项

tan (x)

= tan (x) (sin^{2} (x) - 2)

分解

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

sin^{2} (x) - 2

使用根式运算法则:

a = (a)^{2}

2 = (2)^{2}

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

使用平方差公式:

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

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

= (sin (x) + 2) (sin (x) - 2)

= tan (x) (sin (x) + 2) (sin (x) - 2)

tan (x) (sin (x) + 2) (sin (x) - 2) = 0

分别求解每个部分

tan (x) = 0 or sin (x) + 2 = 0 or sin (x) - 2 = 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

sin (x) + 2 = 0 :

无解

sin (x) + 2 = 0

将

2

到右边

sin (x) + 2 = 0

两边减去

2

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

化简

sin (x) = - 2

sin (x) = - 2

- 1 \leq sin (x) \leq 1

无解

sin (x) - 2 = 0 :

无解

sin (x) - 2 = 0

将

2

到右边

sin (x) - 2 = 0

两边加上

2

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

化简

sin (x) = 2

sin (x) = 2

- 1 \leq sin (x) \leq 1

无解

合并所有解

x = πn

作图

流行的例子

tan (\frac{x}{2}) = 0

csc^2(x)+cot(x)=1

csc^{2} (x) + cot (x) = 1

cos (θ) = - \frac{1}{6}

arcsin (x) = 1

sin(θ)=(sqrt(5))/3

sin (θ) = \frac{5}{3}