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受欢迎的三角函数 >

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

解答

cos (2 arcsin (\frac{3}{2}))

解答

- \frac{1}{2}

+1

十进制

- 0.5

求解步骤

cos (2 arcsin (\frac{3}{2}))

使用三角恒等式改写:

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

cos (2 arcsin (\frac{3}{2}))

使用倍角公式:

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

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

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

使用三角恒等式改写:

sin (arcsin (\frac{3}{2})) = \frac{3}{2}

利用以下特性:

sin (arcsin (x)) = x

= \frac{3}{2}

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

化简

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

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

2 (\frac{3}{2})^{2} = \frac{3}{2}

2 (\frac{3}{2})^{2}

(\frac{3}{2})^{2} = \frac{3}{2 ^{2}}

(\frac{3}{2})^{2}

使用指数法则:

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

= \frac{( 3 ) ^{2}}{2 ^{2}}

(3)^{2} : 3

使用根式运算法则:

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

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

使用指数法则:

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

= 3^{\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

= 3

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

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

分式相乘:

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

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

数字相乘:

3 \cdot 2 = 6

= \frac{6}{2 ^{2}}

分解

6 : 2 \cdot 3

因式分解

6 = 2 \cdot 3

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

约分:

2

= \frac{3}{2}

= 1 - \frac{3}{2}

将项转换为分式:

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

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

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 2 - 3}{2}

1 \cdot 2 - 3 = - 1

1 \cdot 2 - 3

数字相乘:

1 \cdot 2 = 2

= 2 - 3

数字相减:

2 - 3 = - 1

= - 1

= \frac{- 1}{2}

使用分式法则:

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

= - \frac{1}{2}

= - \frac{1}{2}

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