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受欢迎的三角函数 >

1/(cos^2(x))+(1/(2cos(x)))=0

解答

\frac{1}{cos ^{2} ( x )} + (\frac{1}{2 cos ( x )}) = 0

解答

x \in R 无解

求解步骤

\frac{1}{cos ^{2} ( x )} + (\frac{1}{2 cos ( x )}) = 0

用替代法求解

\frac{1}{cos ^{2} ( x )} + \frac{1}{2 cos ( x )} = 0

令

: cos (x) = u

\frac{1}{u ^{2}} + \frac{1}{2 u} = 0

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

\frac{1}{u ^{2}} + \frac{1}{2 u} = 0

乘以最小公倍数

\frac{1}{u ^{2}} + \frac{1}{2 u} = 0

找到

u^{2}, 2 u

的最小公倍数:

2 u^{2}

u^{2}, 2 u

最小公倍数 (LCM)

计算出由出现在

u^{2}

或

2 u

中的因子组成的表达式

= 2 u^{2}

乘以最小公倍数=

2 u^{2}

\frac{1}{u ^{2}} \cdot 2 u^{2} + \frac{1}{2 u} \cdot 2 u^{2} = 0 \cdot 2 u^{2}

化简

\frac{1}{u ^{2}} \cdot 2 u^{2} + \frac{1}{2 u} \cdot 2 u^{2} = 0 \cdot 2 u^{2}

化简

\frac{1}{u ^{2}} \cdot 2 u^{2} : 2

\frac{1}{u ^{2}} \cdot 2 u^{2}

分式相乘:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

约分:

u^{2}

= 1 \cdot 2

数字相乘:

1 \cdot 2 = 2

= 2

化简

\frac{1}{2 u} \cdot 2 u^{2} : u

\frac{1}{2 u} \cdot 2 u^{2}

分式相乘:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

约分:

2

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

乘以:

1 \cdot u^{2} = u^{2}

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

约分:

u

= u

化简

0 \cdot 2 u^{2} : 0

0 \cdot 2 u^{2}

使用法则

0 \cdot a = 0

= 0

2 + u = 0

2 + u = 0

2 + u = 0

将

2

到右边

2 + u = 0

两边减去

2

2 + u - 2 = 0 - 2

化简

u = - 2

u = - 2

验证解

找到无定义的点（奇点）:

u = 0

取

\frac{1}{u ^{2}} + \frac{1}{2 u}

的分母，令其等于零

解

u^{2} = 0 : u = 0

u^{2} = 0

使用法则

x^{n} = 0 \Rightarrow x = 0

u = 0

解

2 u = 0 : u = 0

2 u = 0

两边除以

2

2 u = 0

两边除以

2

\frac{2 u}{2} = \frac{0}{2}

化简

u = 0

u = 0

以下点无定义

u = 0

将不在定义域的点与解相综合:

u = - 2

u = cos (x)

代回

cos (x) = - 2

cos (x) = - 2

cos (x) = - 2 :

无解

cos (x) = - 2

- 1 \leq cos (x) \leq 1

无解

合并所有解

x \in R 无解

作图

流行的例子

cos(α)=sqrt((1+1/5)/2)

(tan(x))(sin^2(x)-a)(sec(x)-a)=0,0<a<1

sin(pi/2 (x+1))= 2/5

sin(*+pi/2)=cos(x)

sin(θ)=(0.000069)2(500*10^{-9})