What is the value of -csch^2(2)tanh(2) ?

The value of -csch^2(2)tanh(2) is -(4e^8-4e^4)/(e^{12)-e^8-e^4+1}

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-csch^2(2)tanh(2)

- csch^{2} (2) tanh (2)

- \frac{4 e ^{8} - 4 e ^{4}}{e ^{12} - e ^{8} - e ^{4} + 1}

Solution steps

- csch^{2} (2) tanh (2)

Rewrite using trig identities:

csch (2) = \frac{2 e ^{2}}{e ^{4} - 1}

= - (\frac{2 e ^{2}}{e ^{4} - 1})^{2} tanh (2)

- (\frac{2 e ^{2}}{e ^{4} - 1})^{2} tanh (2) = - \frac{4 e ^{4} tanh ( 2 )}{( e ^{4} - 1 ) ^{2}}

= - \frac{4 e ^{4} tanh ( 2 )}{( e ^{4} - 1 ) ^{2}}

Rewrite using trig identities:

tanh (2) = \frac{e ^{4} - 1}{e ^{4} + 1}

= - \frac{4 e ^{4} \frac{e ^{4} - 1}{e ^{4} + 1}}{( e ^{4} - 1 ) ^{2}}

Simplify

- \frac{4 e ^{4} \frac{e ^{4} - 1}{e ^{4} + 1}}{( e ^{4} - 1 ) ^{2}} : - \frac{4 e ^{8} - 4 e ^{4}}{e ^{12} - e ^{8} - e ^{4} + 1}

= - \frac{4 e ^{8} - 4 e ^{4}}{e ^{12} - e ^{8} - e ^{4} + 1}

5 \cdot tan (7 8^{\circ})

tan^{2} (3)

\frac{5}{tan ( 4 5 ^{\circ} )}

3 tan (\frac{π}{6})

\frac{4 sin ( 15 0 ^{\circ} )}{6}

What is the value of -csch^2(2)tanh(2) ?
The value of -csch^2(2)tanh(2) is -(4e^8-4e^4)/(e^{12)-e^8-e^4+1}