What is the value of 20(sinh(30/20)-sinh(-30/20)) ?

The value of 20(sinh(30/20)-sinh(-30/20)) is (20(e^3-1))/(e^{3/2)}

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20(sinh(30/20)-sinh(-30/20))

20 (sinh (\frac{30}{20}) - sinh (- \frac{30}{20}))

\frac{20 ( e ^{3} - 1 )}{e ^{\frac{3}{2}}}

Solution steps

20 (sinh (\frac{30}{20}) - sinh (- \frac{30}{20}))

Simplify:

\frac{30}{20} = \frac{3}{2}

Simplify:

- \frac{30}{20} = - \frac{3}{2}

= 20 (sinh (\frac{3}{2}) - sinh (- \frac{3}{2}))

Use the following property:

sinh (- x) = - sinh (x)

sinh (- \frac{3}{2}) = - sinh (\frac{3}{2})

= 20 (sinh (\frac{3}{2}) - (- sinh (\frac{3}{2})))

Simplify

= 40 sinh (\frac{3}{2})

Rewrite using trig identities:

sinh (\frac{3}{2}) = \frac{e ^{3} - 1}{2 e ^{\frac{3}{2}}}

= 40 \cdot \frac{e ^{3} - 1}{2 e ^{\frac{3}{2}}}

Simplify

40 \cdot \frac{e ^{3} - 1}{2 e ^{\frac{3}{2}}} : \frac{20 ( e ^{3} - 1 )}{e ^{\frac{3}{2}}}

= \frac{20 ( e ^{3} - 1 )}{e ^{\frac{3}{2}}}

4 cos (8 0^{\circ})

sin (- 1 (\frac{1}{2}))

arctan (4.9)

\frac{1}{4} sin (π)

sec (\frac{π}{3}) + 2 csc (\frac{π}{6})

What is the value of 20(sinh(30/20)-sinh(-30/20)) ?
The value of 20(sinh(30/20)-sinh(-30/20)) is (20(e^3-1))/(e^{3/2)}