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受欢迎的三角函数 >

(tan^2(x)-4)/(cos(x)+5)=0

解答

\frac{tan ^{2} ( x ) - 4}{cos ( x ) + 5} = 0

解答

x = 1.10714 \dots + πn, x = - 1.10714 \dots + πn

+1

度数

x = 63.43494 \dots^{\circ} + 18 0^{\circ} n, x = - 63.43494 \dots^{\circ} + 18 0^{\circ} n

求解步骤

\frac{tan ^{2} ( x ) - 4}{cos ( x ) + 5} = 0

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

tan^{2} (x) - 4 = 0

用替代法求解

tan^{2} (x) - 4 = 0

令

: tan (x) = u

u^{2} - 4 = 0

u^{2} - 4 = 0 : u = 2, u = - 2

u^{2} - 4 = 0

将

4

到右边

u^{2} - 4 = 0

两边加上

4

u^{2} - 4 + 4 = 0 + 4

化简

u^{2} = 4

u^{2} = 4

对于

x^{2} = f (a)

解为

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

u = 4, u = - 4

4 = 2

4

因式分解数字:

4 = 2^{2}

= 2^{2}

使用根式运算法则:

n a^{n} = a

2^{2} = 2

= 2

- 4 = - 2

- 4

4 = 2

4

因式分解数字:

4 = 2^{2}

= 2^{2}

使用根式运算法则:

n a^{n} = a

2^{2} = 2

= 2

= - 2

u = 2, u = - 2

u = tan (x)

代回

tan (x) = 2, tan (x) = - 2

tan (x) = 2, tan (x) = - 2

tan (x) = 2 : x = arctan (2) + πn

tan (x) = 2

使用反三角函数性质

tan (x) = 2

tan (x) = 2

的通解

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

x = arctan (2) + πn

x = arctan (2) + πn

tan (x) = - 2 : x = arctan (- 2) + πn

tan (x) = - 2

使用反三角函数性质

tan (x) = - 2

tan (x) = - 2

的通解

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

x = arctan (- 2) + πn

x = arctan (- 2) + πn

合并所有解

x = arctan (2) + πn, x = arctan (- 2) + πn

以小数形式表示解

x = 1.10714 \dots + πn, x = - 1.10714 \dots + πn

作图

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