zs

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

受欢迎的三角函数 >

cosh(ln(9))

解答

cosh (ln (9))

解答

\frac{41}{9}

+1

十进制

4.55555 \dots

求解步骤

cosh (ln (9))

化简:

ln (9) = 2 ln (3)

ln (9)

改写

9

为幂形式:

9 = 3^{2}

= ln (3^{2})

使用对数计算法则:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (3^{2}) = 2 ln (3)

= 2 ln (3)

= cosh (2 ln (3))

使用三角恒等式改写:

\frac{41}{9}

cosh (2 ln (3))

使用双曲函数恒等式:

cosh (x) = \frac{e ^{x} + e ^{- x}}{2}

= \frac{e ^{2 l n (3)} + e ^{- 2 l n (3)}}{2}

\frac{e ^{2 l n (3)} + e ^{- 2 l n (3)}}{2} = \frac{41}{9}

\frac{e ^{2 l n (3)} + e ^{- 2 l n (3)}}{2}

e^{2 l n (3)} = 3^{2}

e^{2 l n (3)}

使用指数法则:

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

= (e^{l n (3)})^{2}

使用对数计算法则:

a^{l o g_{a} (b)} = b

e^{l n (3)} = 3

= 3^{2}

e^{- 2 l n (3)} = 3^{- 2}

e^{- 2 l n (3)}

使用指数法则:

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

= (e^{l n (3)})^{- 2}

使用对数计算法则:

a^{l o g_{a} (b)} = b

e^{l n (3)} = 3

= 3^{- 2}

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

化简

\frac{3 ^{2} + 3 ^{- 2}}{2}

3^{2} = 9

= \frac{9 + 3 ^{- 2}}{2}

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

3^{- 2}

使用指数法则:

a^{- b} = \frac{1}{a ^{b}}

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

3^{2} = 9

= \frac{1}{9}

= \frac{9 + \frac{1}{9}}{2}

化简

9 + \frac{1}{9} : \frac{82}{9}

9 + \frac{1}{9}

将项转换为分式:

9 = \frac{9 \cdot 9}{9}

= \frac{9 \cdot 9}{9} + \frac{1}{9}

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{9 \cdot 9 + 1}{9}

9 \cdot 9 + 1 = 82

9 \cdot 9 + 1

数字相乘:

9 \cdot 9 = 81

= 81 + 1

数字相加:

81 + 1 = 82

= 82

= \frac{82}{9}

= \frac{\frac{82}{9}}{2}

使用分式法则:

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

= \frac{82}{9 \cdot 2}

数字相乘:

9 \cdot 2 = 18

= \frac{82}{18}

约分:

2

= \frac{41}{9}

= \frac{41}{9}

= \frac{41}{9}

= \frac{41}{9}

流行的例子

csc (42 0^{\circ})

sin(arcsin(0.9))

sin (arcsin (0.9))

cos (- 5)

csc (\frac{1}{2})

12 cos (6 0^{\circ})