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受欢迎的三角函数 >

arctan(x)+arctan(2)=arctan(7)

解答

arctan (x) + arctan (2) = arctan (7)

解答

x = \frac{1}{3}

求解步骤

arctan (x) + arctan (2) = arctan (7)

将

arctan (2)

到右边

arctan (x) + arctan (2) = arctan (7)

两边减去

arctan (2)

arctan (x) + arctan (2) - arctan (2) = arctan (7) - arctan (2)

化简

arctan (x) = arctan (7) - arctan (2)

arctan (x) = arctan (7) - arctan (2)

使用反三角函数性质

arctan (x) = arctan (7) - arctan (2)

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

x = tan (arctan (7) - arctan (2))

tan (arctan (7) - arctan (2)) = \frac{1}{3}

tan (arctan (7) - arctan (2))

使用三角恒等式改写:

arctan (7) - arctan (2) = arctan (\frac{1}{3})

arctan (7) - arctan (2)

使用和差化积恒等式:

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

= arctan (\frac{7 - 2}{1 + 7 \cdot 2})

化简:

\frac{7 - 2}{1 + 7 \cdot 2} = \frac{1}{3}

\frac{7 - 2}{1 + 7 \cdot 2}

数字相减:

7 - 2 = 5

= \frac{5}{1 + 7 \cdot 2}

1 + 7 \cdot 2 = 15

1 + 7 \cdot 2

数字相乘:

7 \cdot 2 = 14

= 1 + 14

数字相加:

1 + 14 = 15

= 15

= \frac{5}{15}

约分:

5

= \frac{1}{3}

= arctan (\frac{1}{3})

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

使用三角恒等式改写:

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

利用以下特性:

tan (arctan (x)) = x

= \frac{1}{3}

= \frac{1}{3}

x = \frac{1}{3}

x = \frac{1}{3}

作图

流行的例子

3 sec (x) - 1 = 2

sin^{2} (x) = \frac{1}{9}

tan (x) = 0.327

1.04cos^2(θ)+0.102cos(θ)-0.935=0

1.04 cos^{2} (θ) + 0.102 cos (θ) - 0.935 = 0

4 sin (θ) + 4 = 0