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受欢迎的三角函数 >

arctan(4)-arctan(3/5)

解答

arctan (4) - arctan (\frac{3}{5})

解答

\frac{π}{4}

+1

十进制

45

求解步骤

arctan (4) - arctan (\frac{3}{5})

使用三角恒等式改写:

arctan (1)

arctan (4) - arctan (\frac{3}{5})

使用和差化积恒等式:

arctan (s) - arctan (t) = arctan (\frac{s - t}{1 + s t})

= arctan (\frac{4 - \frac{3}{5}}{1 + 4 \cdot \frac{3}{5}})

化简:

\frac{4 - \frac{3}{5}}{1 + 4 \cdot \frac{3}{5}} = 1

\frac{4 - \frac{3}{5}}{1 + 4 \cdot \frac{3}{5}}

4 \cdot \frac{3}{5} = \frac{12}{5}

4 \cdot \frac{3}{5}

分式相乘:

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

= \frac{3 \cdot 4}{5}

数字相乘:

3 \cdot 4 = 12

= \frac{12}{5}

= \frac{4 - \frac{3}{5}}{1 + \frac{12}{5}}

化简

4 - \frac{3}{5} : \frac{17}{5}

4 - \frac{3}{5}

将项转换为分式:

4 = \frac{4 \cdot 5}{5}

= \frac{4 \cdot 5}{5} - \frac{3}{5}

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{4 \cdot 5 - 3}{5}

4 \cdot 5 - 3 = 17

4 \cdot 5 - 3

数字相乘:

4 \cdot 5 = 20

= 20 - 3

数字相减:

20 - 3 = 17

= 17

= \frac{17}{5}

= \frac{\frac{17}{5}}{1 + \frac{12}{5}}

使用分式法则:

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

= \frac{17}{5 ( 1 + \frac{12}{5} )}

化简

1 + \frac{12}{5} : \frac{17}{5}

1 + \frac{12}{5}

将项转换为分式:

1 = \frac{1 \cdot 5}{5}

= \frac{1 \cdot 5}{5} + \frac{12}{5}

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{1 \cdot 5 + 12}{5}

1 \cdot 5 + 12 = 17

1 \cdot 5 + 12

数字相乘:

1 \cdot 5 = 5

= 5 + 12

数字相加:

5 + 12 = 17

= 17

= \frac{17}{5}

= \frac{17}{5 \cdot \frac{17}{5}}

乘

5 \cdot \frac{17}{5} : 17

5 \cdot \frac{17}{5}

分式相乘:

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

= \frac{17 \cdot 5}{5}

约分:

5

= 17

= \frac{17}{17}

使用法则

\frac{a}{a} = 1

= 1

= arctan (1)

= arctan (1)

使用以下普通恒等式:

arctan (1) = \frac{π}{4}

arctan (1)

x 0 \frac{3}{3} 13 arctan (x) 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} arctan (x) 0^{\circ} 3 0^{\circ} 4 5^{\circ} 6 0^{\circ}

= \frac{π}{4}

= \frac{π}{4}

流行的例子

cos (48.5 9^{\circ})

sec(60)+csc(30)

sec (6 0^{\circ}) + csc (3 0^{\circ})

\frac{1}{cos ( 5 0 ^{\circ} )}

sin (4 5^{\circ}) 16

tan(arcsin(-2/5))

tan (arcsin (- \frac{2}{5}))