What is the value of -2arccsch(-2) ?

The value of -2arccsch(-2) is 2ln((1+sqrt(5))/2)

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-2arccsch(-2)

- 2 arccsch (- 2)

2 ln (\frac{1 + 5}{2})

Decimal Notation

0.96242 \dots

Solution steps

- 2 arccsch (- 2)

Use the following property:

arccsch (- x) = - arccsch (x)

arccsch (- 2) = - arccsch (2)

= - 2 (- arccsch (2))

Simplify

= 2 arccsch (2)

Rewrite using trig identities:

arccsch (2) = ln (\frac{1 + 5}{2})

arccsch (2)

Use the Hyperbolic identity:

arccsch (x) = ln (\frac{1}{x} + \frac{1}{x ^{2}} + 1)

= ln (\frac{1}{2} + \frac{1}{2 ^{2}} + 1)

ln (\frac{1}{2} + \frac{1}{2 ^{2}} + 1) = ln (\frac{1 + 5}{2})

ln (\frac{1}{2} + \frac{1}{2 ^{2}} + 1)

\frac{1}{2 ^{2}} + 1 = \frac{5}{2}

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

2^{2} = 4

= \frac{1}{4} + 1

Join

\frac{1}{4} + 1 : \frac{5}{4}

\frac{1}{4} + 1

Convert element to fraction:

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

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

Since the denominators are equal, combine the fractions:

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

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

1 + 1 \cdot 4 = 5

1 + 1 \cdot 4

Multiply the numbers:

1 \cdot 4 = 4

= 1 + 4

Add the numbers:

1 + 4 = 5

= 5

= \frac{5}{4}

= \frac{5}{4}

Apply radical rule:

assuming

a \geq 0, b \geq 0

= \frac{5}{4}

4 = 2

4

Factor the number:

4 = 2^{2}

= 2^{2}

Apply radical rule:

2^{2} = 2

= 2

= \frac{5}{2}

= ln (\frac{1}{2} + \frac{5}{2})

Join

\frac{1}{2} + \frac{5}{2} : \frac{1 + 5}{2}

\frac{1}{2} + \frac{5}{2}

Since the denominators are equal, combine the fractions:

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

= \frac{1 + 5}{2}

= ln (\frac{1 + 5}{2})

= ln (\frac{1 + 5}{2})

= 2 ln (\frac{1 + 5}{2})

5 + 5 cos (\frac{3 π}{4})

sin^{3} (\frac{1}{2} π)

81 (cos (\frac{3 π}{8}) + i sin (\frac{3 π}{8}))

6 \cdot sin (\frac{π}{4})

tan (\frac{9}{4} π)

What is the value of -2arccsch(-2) ?
The value of -2arccsch(-2) is 2ln((1+sqrt(5))/2)