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

The value of 2sinh(ln(2)) is 3/2

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Popular Trigonometry >

2sinh(ln(2))

Solution

2 sinh (ln (2))

Solution

\frac{3}{2}

Decimal

1.5

Solution steps

2 sinh (ln (2))

Rewrite using trig identities:

sinh (ln (2)) = \frac{3}{4}

sinh (ln (2))

Use the Hyperbolic identity:

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

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

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

\frac{e ^{l n (2)} - e ^{- l n (2)}}{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 ^{- 1}}{2}

Simplify

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

Apply exponent rule:

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

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

Apply the fraction rule:

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

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

Multiply the numbers:

2 \cdot 2 = 4

= \frac{3}{4}

= \frac{3}{4}

= \frac{3}{4}

= 2 \cdot \frac{3}{4}

Simplify

2 \cdot \frac{3}{4} : \frac{3}{2}

2 \cdot \frac{3}{4}

Convert element to fraction:

2 = \frac{2}{1}

= \frac{2}{1} \cdot \frac{3}{4}

Cross-cancel common factor:

2

2, 4

Greatest Common Divisor (GCD)

Prime factorization of

2 : 2

2

2

is a prime number, therefore no factorization is possible

= 2

Prime factorization of

4 : 2 \cdot 2

4

4

divides by

24 = 2 \cdot 2

= 2 \cdot 2

The prime factors common to

2, 4

are

= 2

= \frac{3}{2}

= \frac{3}{2}

Popular Examples

arccos((sqrt(3))/2-sqrt(3))

Frequently Asked Questions (FAQ)

What is the value of 2sinh(ln(2)) ?
The value of 2sinh(ln(2)) is 3/2