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受欢迎的三角函数 >

2arctan(1/2)-arctan(x)= pi/4

解答

2 arctan (\frac{1}{2}) - arctan (x) = \frac{π}{4}

解答

x = tan (\frac{8 \cdot 0.46364 \dots - π}{4})

求解步骤

2 arctan (\frac{1}{2}) - arctan (x) = \frac{π}{4}

将

2 arctan (\frac{1}{2})

到右边

2 arctan (\frac{1}{2}) - arctan (x) = \frac{π}{4}

两边减去

2 arctan (\frac{1}{2})

2 arctan (\frac{1}{2}) - arctan (x) - 2 arctan (\frac{1}{2}) = \frac{π}{4} - 2 arctan (\frac{1}{2})

化简

- arctan (x) = \frac{π}{4} - 2 arctan (\frac{1}{2})

- arctan (x) = \frac{π}{4} - 2 arctan (\frac{1}{2})

两边除以

- 1

- arctan (x) = \frac{π}{4} - 2 arctan (\frac{1}{2})

两边除以

- 1

\frac{- arctan ( x )}{- 1} = \frac{\frac{π}{4}}{- 1} - \frac{2 arctan ( \frac{1}{2} )}{- 1}

化简

\frac{- arctan ( x )}{- 1} = \frac{\frac{π}{4}}{- 1} - \frac{2 arctan ( \frac{1}{2} )}{- 1}

化简

\frac{- arctan ( x )}{- 1} : arctan (x)

\frac{- arctan ( x )}{- 1}

使用分式法则:

\frac{- a}{- b} = \frac{a}{b}

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

使用法则

\frac{a}{1} = a

= arctan (x)

化简

\frac{\frac{π}{4}}{- 1} - \frac{2 arctan ( \frac{1}{2} )}{- 1} : \frac{8 arctan ( \frac{1}{2} ) - π}{4}

\frac{\frac{π}{4}}{- 1} - \frac{2 arctan ( \frac{1}{2} )}{- 1}

使用法则

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

= \frac{\frac{π}{4} - 2 arctan ( \frac{1}{2} )}{- 1}

使用分式法则:

\frac{- a}{- b} = \frac{a}{b}

\frac{π}{4} - 2 arctan (\frac{1}{2}) = - (2 arctan (\frac{1}{2}) - \frac{π}{4})

= \frac{2 arctan ( \frac{1}{2} ) - \frac{π}{4}}{1}

化简

2 arctan (\frac{1}{2}) - \frac{π}{4} : \frac{8 arctan ( \frac{1}{2} ) - π}{4}

2 arctan (\frac{1}{2}) - \frac{π}{4}

将项转换为分式:

2 arctan (\frac{1}{2}) = \frac{2 arctan ( \frac{1}{2} ) 4}{4}

= \frac{2 arctan ( \frac{1}{2} ) \cdot 4}{4} - \frac{π}{4}

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{2 arctan ( \frac{1}{2} ) \cdot 4 - π}{4}

数字相乘:

2 \cdot 4 = 8

= \frac{8 arctan ( \frac{1}{2} ) - π}{4}

= \frac{\frac{8 a r c t a n ( \frac{1}{2} ) - π}{4}}{1}

使用分式法则:

\frac{a}{1} = a

= \frac{8 arctan ( \frac{1}{2} ) - π}{4}

arctan (x) = \frac{8 arctan ( \frac{1}{2} ) - π}{4}

arctan (x) = \frac{8 arctan ( \frac{1}{2} ) - π}{4}

arctan (x) = \frac{8 arctan ( \frac{1}{2} ) - π}{4}

使用反三角函数性质

arctan (x) = \frac{8 arctan ( \frac{1}{2} ) - π}{4}

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

x = tan (\frac{8 arctan ( \frac{1}{2} ) - π}{4})

x = tan (\frac{8 arctan ( \frac{1}{2} ) - π}{4})

以小数形式表示解

x = tan (\frac{8 \cdot 0.46364 \dots - π}{4})

作图

流行的例子

cos(x)=(2-tan(x))(1+sin(x))

cos (x) = (2 - tan (x)) (1 + sin (x))

sin (θ) = \frac{13}{85}

sin(2x)=((6m-5))/8

sin (2 x) = \frac{( 6 m - 5 )}{8}

cos(θ)= 3/(sqrt(45))

cos (θ) = \frac{3}{45}

cos^{2} (x) = \frac{9}{16}