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受欢迎的三角函数 >

cos(2arcsin(2/5))

解答

cos (2 arcsin (\frac{2}{5}))

解答

\frac{17}{25}

+1

十进制

0.68

求解步骤

cos (2 arcsin (\frac{2}{5}))

使用三角恒等式改写:

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

cos (2 arcsin (\frac{2}{5}))

使用倍角公式:

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

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

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

使用三角恒等式改写:

cos (arcsin (\frac{2}{5})) = \frac{21}{5}

cos (arcsin (\frac{2}{5}))

使用三角恒等式改写:

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

利用以下特性:

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

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

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

化简

= \frac{21}{5}

= 2 (\frac{21}{5})^{2} - 1

化简

2 (\frac{21}{5})^{2} - 1 : \frac{17}{25}

2 (\frac{21}{5})^{2} - 1

2 (\frac{21}{5})^{2} = \frac{42}{25}

2 (\frac{21}{5})^{2}

(\frac{21}{5})^{2} = \frac{21}{5 ^{2}}

(\frac{21}{5})^{2}

使用指数法则:

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

= \frac{( 21 ) ^{2}}{5 ^{2}}

(21)^{2} : 21

使用根式运算法则:

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

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

使用指数法则:

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

= 2 1^{\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

= 21

= \frac{21}{5 ^{2}}

= 2 \cdot \frac{21}{5 ^{2}}

分式相乘:

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

= \frac{21 \cdot 2}{5 ^{2}}

数字相乘:

21 \cdot 2 = 42

= \frac{42}{5 ^{2}}

5^{2} = 25

= \frac{42}{25}

= \frac{42}{25} - 1

将项转换为分式:

1 = \frac{1 \cdot 25}{25}

= - \frac{1 \cdot 25}{25} + \frac{42}{25}

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 25 + 42}{25}

- 1 \cdot 25 + 42 = 17

- 1 \cdot 25 + 42

数字相乘:

1 \cdot 25 = 25

= - 25 + 42

数字相加/相减:

- 25 + 42 = 17

= 17

= \frac{17}{25}

= \frac{17}{25}

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