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受欢迎的三角函数 >

(sqrt(3)tan(x))/(sec(x))-cos(x)=0

解答

\frac{3 tan ( x )}{sec ( x )} - cos (x) = 0

解答

x = \frac{π}{6} + πn

+1

度数

x = 3 0^{\circ} + 18 0^{\circ} n

求解步骤

\frac{3 tan ( x )}{sec ( x )} - cos (x) = 0

化简

\frac{3 tan ( x )}{sec ( x )} - cos (x) : \frac{3 tan ( x ) - cos ( x ) sec ( x )}{sec ( x )}

\frac{3 tan ( x )}{sec ( x )} - cos (x)

将项转换为分式:

cos (x) = \frac{cos ( x ) sec ( x )}{sec ( x )}

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

因为分母相等，所以合并分式:

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

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

\frac{3 tan ( x ) - cos ( x ) sec ( x )}{sec ( x )} = 0

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

3 tan (x) - cos (x) sec (x) = 0

使用三角恒等式改写

3 tan (x) - cos (x) sec (x)

sec (x) cos (x) = 1

sec (x) cos (x)

用 sin, cos 表示

sec (x) cos (x)

使用基本三角恒等式:

sec (x) = \frac{1}{cos ( x )}

= \frac{1}{cos ( x )} cos (x)

\frac{1}{cos ( x )} cos (x) = 1

\frac{1}{cos ( x )} cos (x)

分式相乘:

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

= \frac{1 cos ( x )}{cos ( x )}

约分:

cos (x)

= 1

= 1

= - 1 + 3 tan (x)

- 1 + 3 tan (x) = 0

将

1

到右边

- 1 + 3 tan (x) = 0

两边加上

1

- 1 + 3 tan (x) + 1 = 0 + 1

化简

3 tan (x) = 1

3 tan (x) = 1

两边除以

3

3 tan (x) = 1

两边除以

3

\frac{3 tan ( x )}{3} = \frac{1}{3}

化简

\frac{3 tan ( x )}{3} = \frac{1}{3}

化简

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

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

约分:

3

= tan (x)

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}

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

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

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

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

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}

x = \frac{π}{6} + πn

x = \frac{π}{6} + πn

作图

流行的例子

sec^2(θ)-2tan(θ)=0

sin(2x)-cos(2x)=sqrt(2)

3tan(2x)-sqrt(3)=0

csc^2(x)=3cot(x)+5