What is the value of 2sinh^2(10) ?

The value of 2sinh^2(10) is ((e^{20}-1)^2)/(2e^{20)}

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2sinh^2(10)

2 sinh^{2} (10)

\frac{( e ^{20} - 1 ) ^{2}}{2 e ^{20}}

Decimal Notation

242582596.70489 \dots

Solution steps

2 sinh^{2} (10)

Rewrite using trig identities:

sinh (10) = \frac{e ^{20} - 1}{2 e ^{10}}

sinh (10)

Use the Hyperbolic identity:

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

= \frac{e ^{10} - e ^{- 10}}{2}

\frac{e ^{10} - e ^{- 10}}{2} = \frac{e ^{20} - 1}{2 e ^{10}}

\frac{e ^{10} - e ^{- 10}}{2}

Apply exponent rule:

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

= \frac{e ^{10} - \frac{1}{e ^{10}}}{2}

Join

e^{10} - \frac{1}{e ^{10}} : \frac{e ^{20} - 1}{e ^{10}}

e^{10} - \frac{1}{e ^{10}}

Convert element to fraction:

e^{10} = \frac{e ^{10} e ^{10}}{e ^{10}}

= \frac{e ^{10} e ^{10}}{e ^{10}} - \frac{1}{e ^{10}}

Since the denominators are equal, combine the fractions:

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

= \frac{e ^{10} e ^{10} - 1}{e ^{10}}

e^{10} e^{10} - 1 = e^{20} - 1

e^{10} e^{10} - 1

e^{10} e^{10} = e^{20}

e^{10} e^{10}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

e^{10} e^{10} = e^{10 + 10}

= e^{10 + 10}

Add the numbers:

10 + 10 = 20

= e^{20}

= e^{20} - 1

= \frac{e ^{20} - 1}{e ^{10}}

= \frac{\frac{e ^{20} - 1}{e ^{10}}}{2}

Apply the fraction rule:

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

= \frac{e ^{20} - 1}{e ^{10} \cdot 2}

= \frac{e ^{20} - 1}{2 e ^{10}}

= 2 (\frac{e ^{20} - 1}{2 e ^{10}})^{2}

Simplify

2 (\frac{e ^{20} - 1}{2 e ^{10}})^{2} : \frac{( e ^{20} - 1 ) ^{2}}{2 e ^{20}}

2 (\frac{e ^{20} - 1}{2 e ^{10}})^{2}

(\frac{e ^{20} - 1}{2 e ^{10}})^{2} = \frac{( e ^{20} - 1 ) ^{2}}{2 ^{2} e ^{20}}

(\frac{e ^{20} - 1}{2 e ^{10}})^{2}

Apply exponent rule:

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

= \frac{( e ^{20} - 1 ) ^{2}}{( 2 e ^{10} ) ^{2}}

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

(2 e^{10})^{2} = 2^{2} (e^{10})^{2}

= \frac{( e ^{20} - 1 ) ^{2}}{2 ^{2} ( e ^{10} ) ^{2}}

(e^{10})^{2} : e^{20}

Apply exponent rule:

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

= e^{10 \cdot 2}

Multiply the numbers:

10 \cdot 2 = 20

= e^{20}

= \frac{( e ^{20} - 1 ) ^{2}}{2 ^{2} e ^{20}}

= 2 \cdot \frac{( e ^{20} - 1 ) ^{2}}{2 ^{2} e ^{20}}

Multiply fractions:

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

= \frac{( e ^{20} - 1 ) ^{2} \cdot 2}{2 ^{2} e ^{20}}

Cancel the common factor:

2

= \frac{( e ^{20} - 1 ) ^{2}}{2 e ^{20}}

= \frac{( e ^{20} - 1 ) ^{2}}{2 e ^{20}}

cos (1) - (1) e^{1}

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15 \cdot tan (3 0^{\circ})

\frac{36 sin ( 6 1 ^{\circ} )}{20}

500 cos (12 0^{\circ})

What is the value of 2sinh^2(10) ?
The value of 2sinh^2(10) is ((e^{20}-1)^2)/(2e^{20)}