Prove that $\frac{1 + sinh 2 A + cosh 2 A}{1 - sinh 2 A - cosh 2 A} = - coth A$ $(1+sinh2A+cosh2A)/(1-sinh2A-cosh2A)=-cothA$ ?

Question

Prove that $\frac{1 + sinh 2 A + cosh 2 A}{1 - sinh 2 A - cosh 2 A} = - coth A$ $(1+sinh2A+cosh2A)/(1-sinh2A-cosh2A)=-cothA$ ?

1 Answer

Impact of this question

2564 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-06-15T07:06:47

See the solution below.

Explanation:

We will use the identities $(1 + cosh 2 A) = 2 {cosh}^{2} A$ $(1+cosh2A)=2cosh^2A$ , $(1 - cosh 2 A) = - 2 {sinh}^{2} A$ $(1-cosh2A)=-2sinh^2A$ and $sinh 2 A = 2 sinh A cosh A$ $sinh2A=2sinhAcoshA$ . Hence

$\frac{1 + sinh 2 A + cosh 2 A}{1 - sinh 2 A - cosh 2 A}$ $(1+sinh2A+cosh2A)/(1-sinh2A-cosh2A)$

= $\frac{2 {cosh}^{2} A + 2 sinh A cosh A}{- 2 sinh A cosh A - 2 {sinh}^{2} A}$ $(2cosh^2A+2sinhAcoshA)/(-2sinhAcoshA-2sinh^2A)$

= $\frac{2 cosh A (cosh A + sinh A)}{- 2 sinh A (cosh A + sinh A)}$ $(2coshA(coshA+sinhA))/(-2sinhA(coshA+sinhA))$

= $- \frac{cosh A}{sinh 2 A}$ $-(coshA)/(sinh2A)$

= $- coth A$ $-cothA$

Science

Math

Humanities

... and beyond

Prove that $\frac{1 + sinh 2 A + cosh 2 A}{1 - sinh 2 A - cosh 2 A} = - coth A$ $(1+sinh2A+cosh2A)/(1-sinh2A-cosh2A)=-cothA$ ?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

Prove that 1+sinh2A+cosh2A1−sinh2A−cosh2A=−cothA(1+sinh2A+cosh2A)/(1-sinh2A-cosh2A)=-cothA?

1 Answer

Explanation:

Related questions

Impact of this question

Prove that $\frac{1 + sinh 2 A + cosh 2 A}{1 - sinh 2 A - cosh 2 A} = - coth A$ $(1+sinh2A+cosh2A)/(1-sinh2A-cosh2A)=-cothA$ ?