What is the value of csch(2) ?

The value of csch(2) is (2e^2)/(e^4-1)

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csch(2)

csch (2)

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

Decimal Notation

0.27572 \dots

Solution steps

csch (2)

Use the Hyperbolic identity:

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

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

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

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

Apply exponent rule:

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

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

Apply the fraction rule:

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

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

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

sin (\frac{π}{3}) \cdot cos (\frac{π}{3})

sin (\frac{2 π}{11})

sin (10000 0^{\circ})

sin (\frac{1}{5})

- sec (\frac{- π}{3})