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受欢迎的三角函数 >

cosh(ln(4))

解答

cosh (ln (4))

解答

\frac{17}{8}

+1

十进制

2.125

求解步骤

cosh (ln (4))

化简:

ln (4) = 2 ln (2)

ln (4)

改写

4

为幂形式:

4 = 2^{2}

= ln (2^{2})

使用对数计算法则:

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

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

= 2 ln (2)

= cosh (2 ln (2))

使用三角恒等式改写:

\frac{17}{8}

cosh (2 ln (2))

使用双曲函数恒等式:

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

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

\frac{e ^{2 l n (2)} + e ^{- 2 l n (2)}}{2} = \frac{17}{8}

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

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

e^{2 l n (2)}

使用指数法则:

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

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

使用对数计算法则:

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

e^{l n (2)} = 2

= 2^{2}

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

e^{- 2 l n (2)}

使用指数法则:

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

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

使用对数计算法则:

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

e^{l n (2)} = 2

= 2^{- 2}

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

化简

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

2^{2} = 4

= \frac{4 + 2 ^{- 2}}{2}

2^{- 2} = \frac{1}{4}

2^{- 2}

使用指数法则:

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

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

2^{2} = 4

= \frac{1}{4}

= \frac{4 + \frac{1}{4}}{2}

化简

4 + \frac{1}{4} : \frac{17}{4}

4 + \frac{1}{4}

将项转换为分式:

4 = \frac{4 \cdot 4}{4}

= \frac{4 \cdot 4}{4} + \frac{1}{4}

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{4 \cdot 4 + 1}{4}

4 \cdot 4 + 1 = 17

4 \cdot 4 + 1

数字相乘:

4 \cdot 4 = 16

= 16 + 1

数字相加:

16 + 1 = 17

= 17

= \frac{17}{4}

= \frac{\frac{17}{4}}{2}

使用分式法则:

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

= \frac{17}{4 \cdot 2}

数字相乘:

4 \cdot 2 = 8

= \frac{17}{8}

= \frac{17}{8}

= \frac{17}{8}

= \frac{17}{8}

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