What is the value of 30cosh(5/30)-28 ?

The value of 30cosh(5/30)-28 is (15(e^{1/6}\sqrt[6]{e}+1)-28\sqrt[6]{e})/(\sqrt[6]{e)}

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30cosh(5/30)-28

30 cosh (\frac{5}{30}) - 28

Decimal Notation

2.41763 \dots

Solution steps

30 cosh (\frac{5}{30}) - 28

Simplify:

\frac{5}{30} = \frac{1}{6}

\frac{5}{30}

Cancel the common factor:

5

= \frac{1}{6}

= 30 cosh (\frac{1}{6}) - 28

Rewrite using trig identities:

cosh (\frac{1}{6})

Use the Hyperbolic identity:

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

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

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

Apply exponent rule:

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

Join

Convert element to fraction:

Since the denominators are equal, combine the fractions:

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

Apply the fraction rule:

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

Multiply fractions:

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

Divide the numbers:

\frac{30}{2} = 15

Convert element to fraction:

Since the denominators are equal, combine the fractions:

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

arctan (\frac{- 25}{\frac{- 80 - 50}{2}})

arccsc (- \frac{4}{3})

cot (3 0^{\circ}) \cdot 7

arctan (3.4)

10 sin (- 3 0^{\circ})

What is the value of 30cosh(5/30)-28 ?
The value of 30cosh(5/30)-28 is (15(e^{1/6}\sqrt[6]{e}+1)-28\sqrt[6]{e})/(\sqrt[6]{e)}