What is the value of cosh(-3)-2+(-3) ?

The value of cosh(-3)-2+(-3) is (e^6+1)/(2e^3)-5

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cosh(-3)-2+(-3)

cosh (- 3) - 2 + (- 3)

\frac{e ^{6} + 1}{2 e ^{3}} - 5

Decimal Notation

5.06766 \dots

Solution steps

cosh (- 3) - 2 + (- 3)

= cosh (- 3) - 2 - 3

Rewrite using trig identities:

cosh (- 3) = \frac{e ^{6} + 1}{2 e ^{3}}

cosh (- 3)

Use the following property:

cosh (- x) = cosh (x)

cosh (- 3) = cosh (3)

= cosh (3)

Rewrite using trig identities:

\frac{e ^{6} + 1}{2 e ^{3}}

cosh (3)

Use the Hyperbolic identity:

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

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

\frac{e ^{3} + e ^{- 3}}{2} = \frac{e ^{6} + 1}{2 e ^{3}}

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

Apply exponent rule:

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

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

Join

e^{3} + \frac{1}{e ^{3}} : \frac{e ^{6} + 1}{e ^{3}}

e^{3} + \frac{1}{e ^{3}}

Convert element to fraction:

e^{3} = \frac{e ^{3} e ^{3}}{e ^{3}}

= \frac{e ^{3} e ^{3}}{e ^{3}} + \frac{1}{e ^{3}}

Since the denominators are equal, combine the fractions:

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

= \frac{e ^{3} e ^{3} + 1}{e ^{3}}

e^{3} e^{3} + 1 = e^{6} + 1

e^{3} e^{3} + 1

e^{3} e^{3} = e^{6}

e^{3} e^{3}

Apply exponent rule:

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

e^{3} e^{3} = e^{3 + 3}

= e^{3 + 3}

Add the numbers:

3 + 3 = 6

= e^{6}

= e^{6} + 1

= \frac{e ^{6} + 1}{e ^{3}}

= \frac{\frac{e ^{6} + 1}{e ^{3}}}{2}

Apply the fraction rule:

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

= \frac{e ^{6} + 1}{e ^{3} \cdot 2}

= \frac{e ^{6} + 1}{2 e ^{3}}

= \frac{e ^{6} + 1}{2 e ^{3}}

= \frac{e ^{6} + 1}{2 e ^{3}} - 2 - 3

Simplify

= \frac{e ^{6} + 1}{2 e ^{3}} - 5

sin (arctan (\frac{20}{21}))

tan (0.35)

\frac{1}{tan ( 1 5 ^{\circ} )}

tan (0.32)

sin (2 0^{\circ}) cos (2 0^{\circ})

What is the value of cosh(-3)-2+(-3) ?
The value of cosh(-3)-2+(-3) is (e^6+1)/(2e^3)-5