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受欢迎的三角函数 >

tan(2x-30)cot(50)=1

解答

tan (2 x - 3 0^{\circ}) cot (5 0^{\circ}) = 1

解答

x = \frac{18 0 ^{\circ} n}{2} + 4 0^{\circ}

+1

弧度

x = \frac{2 π}{9} + \frac{π}{2} n

求解步骤

tan (2 x - 3 0^{\circ}) cot (5 0^{\circ}) = 1

两边除以

cot (5 0^{\circ})

tan (2 x - 3 0^{\circ}) cot (5 0^{\circ}) = 1

两边除以

cot (5 0^{\circ})

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

化简

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

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

使用反三角函数性质

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

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

的通解

tan (x) = a \Rightarrow x = arctan (a) + 18 0^{\circ} n

2 x - 3 0^{\circ} = arctan (\frac{1}{cot ( 5 0 ^{\circ} )}) + 18 0^{\circ} n

2 x - 3 0^{\circ} = arctan (\frac{1}{cot ( 5 0 ^{\circ} )}) + 18 0^{\circ} n

解

2 x - 3 0^{\circ} = arctan (\frac{1}{cot ( 5 0 ^{\circ} )}) + 18 0^{\circ} n : x = \frac{18 0 ^{\circ} n}{2} + 4 0^{\circ}

2 x - 3 0^{\circ} = arctan (\frac{1}{cot ( 5 0 ^{\circ} )}) + 18 0^{\circ} n

化简

arctan (\frac{1}{cot ( 5 0 ^{\circ} )}) + 18 0^{\circ} n : 5 0^{\circ} + 18 0^{\circ} n

arctan (\frac{1}{cot ( 5 0 ^{\circ} )}) + 18 0^{\circ} n

arctan (\frac{1}{cot ( 5 0 ^{\circ} )}) = 5 0^{\circ}

arctan (\frac{1}{cot ( 5 0 ^{\circ} )})

使用三角恒等式改写:

cot (5 0^{\circ}) = \frac{1}{tan ( 5 0 ^{\circ} )}

cot (5 0^{\circ})

使用基本三角恒等式:

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

= \frac{1}{tan ( 5 0 ^{\circ} )}

= arctan (\frac{1}{\frac{1}{t a n ( 5 0 ^{\circ} )}})

化简

= arctan (tan (5 0^{\circ}))

Use the inverse trig property:

5 0^{\circ}

arctan (tan (5 0^{\circ}))

对于

- 9 0^{\circ} < x < 9 0^{\circ}, a rc t an (t an (x)) = x

- 9 0^{\circ} < 5 0^{\circ} < 9 0^{\circ}

= 5 0^{\circ}

= 5 0^{\circ}

= 5 0^{\circ} + 18 0^{\circ} n

2 x - 3 0^{\circ} = 5 0^{\circ} + 18 0^{\circ} n

将

3 0^{\circ}

到右边

2 x - 3 0^{\circ} = 5 0^{\circ} + 18 0^{\circ} n

两边加上

3 0^{\circ}

2 x - 3 0^{\circ} + 3 0^{\circ} = 5 0^{\circ} + 18 0^{\circ} n + 3 0^{\circ}

化简

2 x - 3 0^{\circ} + 3 0^{\circ} = 5 0^{\circ} + 18 0^{\circ} n + 3 0^{\circ}

化简

2 x - 3 0^{\circ} + 3 0^{\circ} : 2 x

2 x - 3 0^{\circ} + 3 0^{\circ}

同类项相加:

- 3 0^{\circ} + 3 0^{\circ} = 0

= 2 x

化简

5 0^{\circ} + 18 0^{\circ} n + 3 0^{\circ} : 18 0^{\circ} n + 8 0^{\circ}

5 0^{\circ} + 18 0^{\circ} n + 3 0^{\circ}

对同类项分组

= 18 0^{\circ} n + 3 0^{\circ} + 5 0^{\circ}

6, 18

的最小公倍数:

18

6, 18

最小公倍数 (LCM)

6

质因数分解:

2 \cdot 3

6

6

除以

26 = 3 \cdot 2

= 2 \cdot 3

2, 3

都是质数，因此无法进一步因数分解

= 2 \cdot 3

18

质因数分解:

2 \cdot 3 \cdot 3

18

18

除以

218 = 9 \cdot 2

= 2 \cdot 9

9

除以

39 = 3 \cdot 3

= 2 \cdot 3 \cdot 3

2, 3

都是质数，因此无法进一步因数分解

= 2 \cdot 3 \cdot 3

将每个因子乘以它在

6

或

18

中出现的最多次数

= 2 \cdot 3 \cdot 3

数字相乘:

2 \cdot 3 \cdot 3 = 18

= 18

根据最小公倍数调整分式

将每个分子乘以其分母转变为最小公倍数所要乘以的同一数值

18

对于

3 0^{\circ} :

将分母和分子乘以

3

3 0^{\circ} = \frac{18 0 ^{\circ} 3}{6 \cdot 3} = 3 0^{\circ}

= 3 0^{\circ} + 5 0^{\circ}

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{18 0 ^{\circ} 3 + 90 0 ^{\circ}}{18}

同类项相加:

54 0^{\circ} + 90 0^{\circ} = 144 0^{\circ}

= 8 0^{\circ}

约分:

2

= 18 0^{\circ} n + 8 0^{\circ}

2 x = 18 0^{\circ} n + 8 0^{\circ}

2 x = 18 0^{\circ} n + 8 0^{\circ}

2 x = 18 0^{\circ} n + 8 0^{\circ}

两边除以

2

2 x = 18 0^{\circ} n + 8 0^{\circ}

两边除以

2

\frac{2 x}{2} = \frac{18 0 ^{\circ} n}{2} + \frac{8 0 ^{\circ}}{2}

化简

\frac{2 x}{2} = \frac{18 0 ^{\circ} n}{2} + \frac{8 0 ^{\circ}}{2}

化简

\frac{2 x}{2} : x

\frac{2 x}{2}

数字相除:

\frac{2}{2} = 1

= x

化简

\frac{18 0 ^{\circ} n}{2} + \frac{8 0 ^{\circ}}{2} : \frac{18 0 ^{\circ} n}{2} + 4 0^{\circ}

\frac{18 0 ^{\circ} n}{2} + \frac{8 0 ^{\circ}}{2}

\frac{8 0 ^{\circ}}{2} = 4 0^{\circ}

\frac{8 0 ^{\circ}}{2}

使用分式法则:

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

= \frac{72 0 ^{\circ}}{9 \cdot 2}

数字相乘:

9 \cdot 2 = 18

= 4 0^{\circ}

约分:

2

= 4 0^{\circ}

= \frac{18 0 ^{\circ} n}{2} + 4 0^{\circ}

x = \frac{18 0 ^{\circ} n}{2} + 4 0^{\circ}

x = \frac{18 0 ^{\circ} n}{2} + 4 0^{\circ}

x = \frac{18 0 ^{\circ} n}{2} + 4 0^{\circ}

x = \frac{18 0 ^{\circ} n}{2} + 4 0^{\circ}

作图

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