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受欢迎的三角函数 >

cos(2arcsin(5/13))

解答

cos (2 arcsin (\frac{5}{13}))

解答

\frac{119}{169}

+1

十进制

0.70414 \dots

求解步骤

cos (2 arcsin (\frac{5}{13}))

使用三角恒等式改写:

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

cos (2 arcsin (\frac{5}{13}))

使用倍角公式:

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

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

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

使用三角恒等式改写:

sin (arcsin (\frac{5}{13})) = \frac{5}{13}

利用以下特性:

sin (arcsin (x)) = x

= \frac{5}{13}

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

化简

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

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

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}

= 1 - \frac{50}{169}

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

数字相减:

169 - 50 = 119

= 119

= \frac{119}{169}

= \frac{119}{169}

流行的例子

sin(arccos(1/2))

cos(arcsin((sqrt(3))/2))