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受欢迎的三角函数 >

2arctan(1/2)=arccos(x)

解答

2 arctan (\frac{1}{2}) = arccos (x)

解答

x = \frac{3}{5}

求解步骤

2 arctan (\frac{1}{2}) = arccos (x)

交换两边

arccos (x) = 2 arctan (\frac{1}{2})

使用反三角函数性质

arccos (x) = 2 arctan (\frac{1}{2})

arccos (x) = a \Rightarrow x = cos (a)

x = cos (2 arctan (\frac{1}{2}))

cos (2 arctan (\frac{1}{2})) = \frac{3}{5}

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

使用三角恒等式改写:

1 - 2 sin^{2} (arctan (\frac{1}{2}))

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

使用倍角公式:

cos (2 x) = 1 - 2 sin^{2} (x)

= 1 - 2 sin^{2} (arctan (\frac{1}{2}))

= 1 - 2 sin^{2} (arctan (\frac{1}{2}))

使用三角恒等式改写:

sin (arctan (\frac{1}{2})) = \frac{5}{5}

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

使用三角恒等式改写:

sin (arctan (\frac{1}{2})) = \frac{( \frac{1}{2} ) 1 + ( \frac{1}{2} ) ^{2}}{1 + ( \frac{1}{2} ) ^{2}}

利用以下特性:

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

= \frac{( \frac{1}{2} ) 1 + ( \frac{1}{2} ) ^{2}}{1 + ( \frac{1}{2} ) ^{2}}

= \frac{\frac{1}{2} 1 + ( \frac{1}{2} ) ^{2}}{1 + ( \frac{1}{2} ) ^{2}}

化简

= \frac{5}{5}

= 1 - 2 (\frac{5}{5})^{2}

化简

1 - 2 (\frac{5}{5})^{2} : \frac{3}{5}

1 - 2 (\frac{5}{5})^{2}

2 (\frac{5}{5})^{2} = \frac{2}{5}

2 (\frac{5}{5})^{2}

(\frac{5}{5})^{2} = \frac{1}{5}

(\frac{5}{5})^{2}

使用指数法则:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{( 5 ) ^{2}}{5 ^{2}}

(5)^{2} : 5

使用根式运算法则:

a = a^{\frac{1}{2}}

= (5^{\frac{1}{2}})^{2}

使用指数法则:

(a^{b})^{c} = a^{b c}

= 5^{\frac{1}{2} \cdot 2}

\frac{1}{2} \cdot 2 = 1

\frac{1}{2} \cdot 2

分式相乘:

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

= \frac{1 \cdot 2}{2}

约分:

2

= 1

= 5

= \frac{5}{5 ^{2}}

约分:

5

= \frac{1}{5}

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

分式相乘:

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

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

数字相乘:

1 \cdot 2 = 2

= \frac{2}{5}

= 1 - \frac{2}{5}

将项转换为分式:

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

= \frac{1 \cdot 5}{5} - \frac{2}{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 - 2}{5}

1 \cdot 5 - 2 = 3

1 \cdot 5 - 2

数字相乘:

1 \cdot 5 = 5

= 5 - 2

数字相减:

5 - 2 = 3

= 3

= \frac{3}{5}

= \frac{3}{5}

x = \frac{3}{5}

x = \frac{3}{5}

作图

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