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受欢迎的三角函数 >

(3tan^2(x)-5)/(cos(x)+1)=0

解答

\frac{3 tan ^{2} ( x ) - 5}{cos ( x ) + 1} = 0

解答

x = 0.91173 \dots + πn, x = - 0.91173 \dots + πn

+1

度数

x = 52.23875 \dots^{\circ} + 18 0^{\circ} n, x = - 52.23875 \dots^{\circ} + 18 0^{\circ} n

求解步骤

\frac{3 tan ^{2} ( x ) - 5}{cos ( x ) + 1} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

3 tan^{2} (x) - 5 = 0

用替代法求解

3 tan^{2} (x) - 5 = 0

令

: tan (x) = u

3 u^{2} - 5 = 0

3 u^{2} - 5 = 0 : u = \frac{5}{3}, u = - \frac{5}{3}

3 u^{2} - 5 = 0

将

5

到右边

3 u^{2} - 5 = 0

两边加上

5

3 u^{2} - 5 + 5 = 0 + 5

化简

3 u^{2} = 5

3 u^{2} = 5

两边除以

3

3 u^{2} = 5

两边除以

3

\frac{3 u ^{2}}{3} = \frac{5}{3}

化简

u^{2} = \frac{5}{3}

u^{2} = \frac{5}{3}

对于

x^{2} = f (a)

解为

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

u = \frac{5}{3}, u = - \frac{5}{3}

u = tan (x)

代回

tan (x) = \frac{5}{3}, tan (x) = - \frac{5}{3}

tan (x) = \frac{5}{3}, tan (x) = - \frac{5}{3}

tan (x) = \frac{5}{3} : x = arctan (\frac{5}{3}) + πn

tan (x) = \frac{5}{3}

使用反三角函数性质

tan (x) = \frac{5}{3}

tan (x) = \frac{5}{3}

的通解

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

x = arctan (\frac{5}{3}) + πn

x = arctan (\frac{5}{3}) + πn

tan (x) = - \frac{5}{3} : x = arctan (- \frac{5}{3}) + πn

tan (x) = - \frac{5}{3}

使用反三角函数性质

tan (x) = - \frac{5}{3}

tan (x) = - \frac{5}{3}

的通解

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

x = arctan (- \frac{5}{3}) + πn

x = arctan (- \frac{5}{3}) + πn

合并所有解

x = arctan (\frac{5}{3}) + πn, x = arctan (- \frac{5}{3}) + πn

以小数形式表示解

x = 0.91173 \dots + πn, x = - 0.91173 \dots + πn

作图

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