What is the value of csch(ln(2)) ?

The value of csch(ln(2)) is 4/3

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csch(ln(2))

csch (ln (2))

\frac{4}{3}

Decimal Notation

1.33333 \dots

Solution steps

csch (ln (2))

Use the Hyperbolic identity:

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

= \frac{2}{e ^{l n (2)} - e ^{- l n (2)}}

\frac{2}{e ^{l n (2)} - e ^{- l n (2)}} = \frac{4}{3}

\frac{2}{e ^{l n (2)} - e ^{- l n (2)}}

e^{l n (2)} = 2

e^{l n (2)}

Apply log rule:

a^{l o g_{a} (b)} = b

= 2

e^{- l n (2)} = 2^{- 1}

e^{- l n (2)}

Apply exponent rule:

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

= (e^{l n (2)})^{- 1}

Apply log rule:

a^{l o g_{a} (b)} = b

e^{l n (2)} = 2

= 2^{- 1}

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

Simplify

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

Apply exponent rule:

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

= \frac{2}{2 - \frac{1}{2}}

Join

2 - \frac{1}{2} : \frac{3}{2}

2 - \frac{1}{2}

Convert element to fraction:

2 = \frac{2 \cdot 2}{2}

= \frac{2 \cdot 2}{2} - \frac{1}{2}

Since the denominators are equal, combine the fractions:

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

= \frac{2 \cdot 2 - 1}{2}

2 \cdot 2 - 1 = 3

2 \cdot 2 - 1

Multiply the numbers:

2 \cdot 2 = 4

= 4 - 1

Subtract the numbers:

4 - 1 = 3

= 3

= \frac{3}{2}

= \frac{2}{\frac{3}{2}}

Apply the fraction rule:

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

= \frac{2 \cdot 2}{3}

Multiply the numbers:

2 \cdot 2 = 4

= \frac{4}{3}

= \frac{4}{3}

= \frac{4}{3}

tan (2 x) = 3

x, tan (x) + sec (x) = 2 cos (x)

cos (θ) = - \frac{2}{2}

tan (θ) - 3 cot (θ) = 0

cot (- \frac{π}{2})