Question

Prove that $coth ( x - y) = \frac{coth\ x\ .\ coth\ y\ - \ 1}{coth\ y\ -\ coth\ x}$.

Answer 1

Hi

The required proof is :

$RHS=\frac{cothx.cothy-1}{cothy-cothx}\\ \\RHS=\frac{(coshx/sinhx).(coshy/sinhy)-1}{coshy/sinhy-coshx/sinhx}\\\\\\RHS=\frac{\frac{coshx.coshy-sinhx.sinhy}{sinhx.sinhy} }{\frac{sinhx.coshy-coshx.sinhy}{sinhy.sinhx}}\\\\RHS=\frac{coshx.coshy-sinhx.sinhy}{sinhx.coshy-coshx.sinhy}\\\\\\RHS=\frac{cosh(x-y)}{sinh(x-y)}\\\\RHS=coth(x-y)=LHS$

Hope it will help You.

Answer 2

Step-by-step explanation:

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