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受欢迎的三角函数 >

2tan^2(α)=2tan(α)

解答

2 tan^{2} (α) = 2 tan (α)

解答

α = πn, α = \frac{π}{4} + πn

+1

度数

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

求解步骤

2 tan^{2} (α) = 2 tan (α)

用替代法求解

2 tan^{2} (α) = 2 tan (α)

令

: tan (α) = u

2 u^{2} = 2 u

2 u^{2} = 2 u : u = 0, u = 1

2 u^{2} = 2 u

将

2 u

para o lado esquerdo

2 u^{2} = 2 u

两边减去

2 u

2 u^{2} - 2 u = 2 u - 2 u

化简

2 u^{2} - 2 u = 0

2 u^{2} - 2 u = 0

因式分解

2 u^{2} - 2 u : 2 u (u - 1)

2 u^{2} - 2 u

使用指数法则:

a^{b + c} = a^{b} a^{c}

u^{2} = uu

= 2 uu - 2 u

因式分解出通项

2 u

= 2 u (u - 1)

2 u (u - 1) = 0

使用零因数法则： If

ab = 0

then

a = 0

or

b = 0

u = 0 or u - 1 = 0

解

u - 1 = 0 : u = 1

u - 1 = 0

将

1

到右边

u - 1 = 0

两边加上

1

u - 1 + 1 = 0 + 1

化简

u = 1

u = 1

二次方程组的解是:

u = 0, u = 1

u = tan (α)

代回

tan (α) = 0, tan (α) = 1

tan (α) = 0, tan (α) = 1

tan (α) = 0 : α = πn

tan (α) = 0

tan (α) = 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}

α = 0 + πn

α = 0 + πn

解

α = 0 + πn : α = πn

α = 0 + πn

0 + πn = πn

α = πn

α = πn

tan (α) = 1 : α = \frac{π}{4} + πn

tan (α) = 1

tan (α) = 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}

α = \frac{π}{4} + πn

α = \frac{π}{4} + πn

合并所有解

α = πn, α = \frac{π}{4} + πn

作图

流行的例子

cos^2(x)-sin^2(x)=-3/4

cos^{2} (x) - sin^{2} (x) = - \frac{3}{4}

8 cos (8 x) = 0

sin(x)=2sqrt(2)

sin (x) = 22

sin(x)(1+sin(x))=0

sin (x) (1 + sin (x)) = 0

cos (x) = 10