What is the value of cosh^2(2) ?

The value of cosh^2(2) is ((e^4+1)^2)/(4e^4)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

cosh^2(2)

cosh^{2} (2)

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

Decimal Notation

14.15411 \dots

Solution steps

cosh^{2} (2)

Rewrite using trig identities:

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

cosh (2)

Use the Hyperbolic identity:

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}

Apply exponent rule:

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

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

Join

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

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

Convert element to fraction:

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

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

Since the denominators are equal, combine the fractions:

\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}

Apply exponent rule:

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

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

= e^{2 + 2}

Add the numbers:

2 + 2 = 4

= e^{4}

= e^{4} + 1

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

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

Apply the fraction rule:

\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}

Simplify

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

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

Apply exponent rule:

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

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

Apply exponent rule:

(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}

Apply exponent rule:

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

= e^{2 \cdot 2}

Multiply the numbers:

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}}

cos (12 6^{\circ})

30 \cdot cos (4 0^{\circ})

3 tan^{2} (3 0^{\circ})

\frac{28 ( sin ( 10 2 ^{\circ} ) )}{sin ( 2 9 ^{\circ} )}

sin^{4} (2 π)