sinhx-sinhycoshx-coshy=
2coth(x+y)
tanhx+y2
cothx+y2
cothx-y2
Explanation for the correct answer:
Simplifying the given expression using trigonometric identities:
sinhx-sinhycoshx-coshy=2coshx+y2sinhx-y22sinhx+y2sinhx-y2∵sinx-siny=2cosx+y2sinx-y2andcosx-cosy=2sinhx+y2sinhx-y2=cothx+y2
Thus, sinhx-sinhycoshx-coshy=cothx+y2
Therefore, the correct answer is option (C).