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受欢迎的三角函数 >

cosh^2(2)

解答

cosh^{2} (2)

解答

\frac{( e ^{4} + 1 ) ^{2}}{4 e ^{4}}

+1

十进制

14.15411 \dots

求解步骤

cosh^{2} (2)

使用三角恒等式改写:

cosh (2) = \frac{e ^{4} + 1}{2 e ^{2}}

cosh (2)

使用双曲函数恒等式:

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

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

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

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

使用指数法则:

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

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

化简

e^{2} + \frac{1}{e ^{2}} : \frac{e ^{4} + 1}{e ^{2}}

e^{2} + \frac{1}{e ^{2}}

将项转换为分式:

e^{2} = \frac{e ^{2} e ^{2}}{e ^{2}}

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

e^{2} e^{2} + 1 = e^{4} + 1

e^{2} e^{2} + 1

e^{2} e^{2} = e^{4}

e^{2} e^{2}

使用指数法则:

a^{b} \cdot a^{c} = a^{b + c}

e^{2} e^{2} = e^{2 + 2}

= e^{2 + 2}

数字相加:

2 + 2 = 4

= e^{4}

= e^{4} + 1

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

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

使用分式法则:

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

= \frac{e ^{4} + 1}{e ^{2} \cdot 2}

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

= (\frac{e ^{4} + 1}{2 e ^{2}})^{2}

化简

(\frac{e ^{4} + 1}{2 e ^{2}})^{2} : \frac{( e ^{4} + 1 ) ^{2}}{4 e ^{4}}

(\frac{e ^{4} + 1}{2 e ^{2}})^{2}

使用指数法则:

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

= \frac{( e ^{4} + 1 ) ^{2}}{( 2 e ^{2} ) ^{2}}

使用指数法则:

(a \cdot b)^{n} = a^{n} b^{n}

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

= \frac{( e ^{4} + 1 ) ^{2}}{2 ^{2} ( e ^{2} ) ^{2}}

(e^{2})^{2} : e^{4}

使用指数法则:

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

= e^{2 \cdot 2}

数字相乘:

2 \cdot 2 = 4

= e^{4}

= \frac{( e ^{4} + 1 ) ^{2}}{2 ^{2} e ^{4}}

2^{2} = 4

= \frac{( e ^{4} + 1 ) ^{2}}{4 e ^{4}}

= \frac{( e ^{4} + 1 ) ^{2}}{4 e ^{4}}

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