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受欢迎的三角函数 >

cos(2arcsin(12/13))

解答

cos (2 arcsin (\frac{12}{13}))

解答

- \frac{119}{169}

+1

十进制

- 0.70414 \dots

求解步骤

cos (2 arcsin (\frac{12}{13}))

使用三角恒等式改写:

2 cos^{2} (arcsin (\frac{12}{13})) - 1

cos (2 arcsin (\frac{12}{13}))

使用倍角公式:

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

= 2 cos^{2} (arcsin (\frac{12}{13})) - 1

= 2 cos^{2} (arcsin (\frac{12}{13})) - 1

使用三角恒等式改写:

cos (arcsin (\frac{12}{13})) = \frac{5}{13}

cos (arcsin (\frac{12}{13}))

使用三角恒等式改写:

cos (arcsin (\frac{12}{13})) = 1 - (\frac{12}{13})^{2}

利用以下特性:

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

= 1 - (\frac{12}{13})^{2}

= 1 - (\frac{12}{13})^{2}

化简

= \frac{5}{13}

= 2 (\frac{5}{13})^{2} - 1

化简

2 (\frac{5}{13})^{2} - 1 : - \frac{119}{169}

2 (\frac{5}{13})^{2} - 1

2 (\frac{5}{13})^{2} = \frac{50}{169}

2 (\frac{5}{13})^{2}

(\frac{5}{13})^{2} = \frac{5 ^{2}}{1 3 ^{2}}

(\frac{5}{13})^{2}

使用指数法则:

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

= \frac{5 ^{2}}{1 3 ^{2}}

= 2 \cdot \frac{5 ^{2}}{1 3 ^{2}}

分式相乘:

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

= \frac{5 ^{2} \cdot 2}{1 3 ^{2}}

5^{2} \cdot 2 = 50

5^{2} \cdot 2

5^{2} = 25

= 25 \cdot 2

数字相乘:

25 \cdot 2 = 50

= 50

= \frac{50}{1 3 ^{2}}

1 3^{2} = 169

= \frac{50}{169}

= \frac{50}{169} - 1

将项转换为分式:

1 = \frac{1 \cdot 169}{169}

= - \frac{1 \cdot 169}{169} + \frac{50}{169}

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 169 + 50}{169}

- 1 \cdot 169 + 50 = - 119

- 1 \cdot 169 + 50

数字相乘:

1 \cdot 169 = 169

= - 169 + 50

数字相加/相减:

- 169 + 50 = - 119

= - 119

= \frac{- 119}{169}

使用分式法则:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{119}{169}

= - \frac{119}{169}

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