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受欢迎的三角函数 >

sqrt(3)*tan^2(x)-1=0

解答

3 \cdot tan^{2} (x) - 1 = 0

解答

x = 0.64976 \dots + πn, x = - 0.64976 \dots + πn

+1

度数

x = 37.22886 \dots^{\circ} + 18 0^{\circ} n, x = - 37.22886 \dots^{\circ} + 18 0^{\circ} n

求解步骤

3 tan^{2} (x) - 1 = 0

用替代法求解

3 tan^{2} (x) - 1 = 0

令

: tan (x) = u

3 u^{2} - 1 = 0

3 u^{2} - 1 = 0 : u = \frac{3}{3}, u = - \frac{3}{3}

3 u^{2} - 1 = 0

将

1

到右边

3 u^{2} - 1 = 0

两边加上

1

3 u^{2} - 1 + 1 = 0 + 1

化简

3 u^{2} = 1

3 u^{2} = 1

两边除以

3

3 u^{2} = 1

两边除以

3

\frac{3 u ^{2}}{3} = \frac{1}{3}

化简

\frac{3 u ^{2}}{3} = \frac{1}{3}

化简

\frac{3 u ^{2}}{3} : u^{2}

\frac{3 u ^{2}}{3}

约分:

3

= u^{2}

化简

\frac{1}{3} : \frac{3}{3}

\frac{1}{3}

乘以共轭根式

\frac{3}{3}

= \frac{1 \cdot 3}{3 3}

1 \cdot 3 = 3

33 = 3

33

使用根式运算法则:

a a = a

33 = 3

= 3

= \frac{3}{3}

u^{2} = \frac{3}{3}

u^{2} = \frac{3}{3}

u^{2} = \frac{3}{3}

对于

x^{2} = f (a)

解为

x = f (a), - f (a)

u = \frac{3}{3}, u = - \frac{3}{3}

u = tan (x)

代回

tan (x) = \frac{3}{3}, tan (x) = - \frac{3}{3}

tan (x) = \frac{3}{3}, tan (x) = - \frac{3}{3}

tan (x) = \frac{3}{3} : x = arctan \frac{3}{3} + πn

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

使用反三角函数性质

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

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

的通解

tan (x) = a \Rightarrow x = arctan (a) + πn

x = arctan \frac{3}{3} + πn

x = arctan \frac{3}{3} + πn

tan (x) = - \frac{3}{3} : x = arctan - \frac{3}{3} + πn

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

使用反三角函数性质

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

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

的通解

tan (x) = - a \Rightarrow x = arctan (- a) + πn

x = arctan - \frac{3}{3} + πn

x = arctan - \frac{3}{3} + πn

合并所有解

x = arctan \frac{3}{3} + πn, x = arctan - \frac{3}{3} + πn

以小数形式表示解

x = 0.64976 \dots + πn, x = - 0.64976 \dots + πn

作图

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