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受欢迎的三角函数 >

tan(2arcsin(3/5))

解答

tan (2 arcsin (\frac{3}{5}))

解答

\frac{24}{7}

+1

十进制

3.42857 \dots

求解步骤

tan (2 arcsin (\frac{3}{5}))

使用三角恒等式改写:

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

tan (2 arcsin (\frac{3}{5}))

使用倍角公式:

tan (2 x) = \frac{2 tan ( x )}{1 - tan ^{2} ( x )}

= \frac{2 tan ( arcsin ( \frac{3}{5} ) )}{1 - tan ^{2} ( arcsin ( \frac{3}{5} ) )}

= \frac{2 tan ( arcsin ( \frac{3}{5} ) )}{1 - tan ^{2} ( arcsin ( \frac{3}{5} ) )}

使用三角恒等式改写:

tan (arcsin (\frac{3}{5})) = \frac{3}{4}

tan (arcsin (\frac{3}{5}))

使用三角恒等式改写:

tan (arcsin (\frac{3}{5})) = \frac{( \frac{3}{5} ) 1 - ( \frac{3}{5} ) ^{2}}{1 - ( \frac{3}{5} ) ^{2}}

利用以下特性:

tan (arcsin (x)) = \frac{x 1 - x ^{2}}{1 - x ^{2}}

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

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

化简

= \frac{3}{4}

= \frac{2 \cdot \frac{3}{4}}{1 - ( \frac{3}{4} ) ^{2}}

化简

\frac{2 \cdot \frac{3}{4}}{1 - ( \frac{3}{4} ) ^{2}} : \frac{24}{7}

\frac{2 \cdot \frac{3}{4}}{1 - ( \frac{3}{4} ) ^{2}}

使用指数法则:

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

= \frac{2 \cdot \frac{3}{4}}{1 - \frac{3 ^{2}}{4 ^{2}}}

乘

2 \cdot \frac{3}{4} : \frac{3}{2}

2 \cdot \frac{3}{4}

分式相乘:

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

= \frac{3 \cdot 2}{4}

数字相乘:

3 \cdot 2 = 6

= \frac{6}{4}

约分:

2

= \frac{3}{2}

= \frac{\frac{3}{2}}{1 - \frac{3 ^{2}}{4 ^{2}}}

\frac{3 ^{2}}{4 ^{2}} = \frac{9}{16}

\frac{3 ^{2}}{4 ^{2}}

3^{2} = 9

= \frac{9}{4 ^{2}}

4^{2} = 16

= \frac{9}{16}

= \frac{\frac{3}{2}}{1 - \frac{9}{16}}

使用分式法则:

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

= \frac{3}{2 ( 1 - \frac{9}{16} )}

化简

1 - \frac{9}{16} : \frac{7}{16}

1 - \frac{9}{16}

将项转换为分式:

1 = \frac{1 \cdot 16}{16}

= \frac{1 \cdot 16}{16} - \frac{9}{16}

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 16 - 9}{16}

1 \cdot 16 - 9 = 7

1 \cdot 16 - 9

数字相乘:

1 \cdot 16 = 16

= 16 - 9

数字相减:

16 - 9 = 7

= 7

= \frac{7}{16}

= \frac{3}{2 \cdot \frac{7}{16}}

乘

2 \cdot \frac{7}{16} : \frac{7}{8}

2 \cdot \frac{7}{16}

分式相乘:

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

= \frac{7 \cdot 2}{16}

数字相乘:

7 \cdot 2 = 14

= \frac{14}{16}

约分:

2

= \frac{7}{8}

= \frac{3}{\frac{7}{8}}

使用分式法则:

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

= \frac{3 \cdot 8}{7}

数字相乘:

3 \cdot 8 = 24

= \frac{24}{7}

= \frac{24}{7}

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