sinh3z equals
2sinhz–4sinh3z
4sinh3z–3sinhz
3sinhz+4sinh3z
None of these
Explanation for the correct answer:
Simplifying the given expression using trigonometric identities:
sinh3z=sinh(2z+z)=sinh(2z)coshz+cosh(2z)sinhz[∵sinh(x+y)=sinhxcoshy+coshxsinhy]=(2sinhzcoshz)coshz+(cosh2z+sinh2z)sinhz[∵sinh2x=2sinhxcoshxandcosh2x=cosh2x+sinh2x]=2sinhzcosh2z+(1+sinh2z+sinh2z)sinhz[∵cosh2z=1+sinh2z]=2sinhz(1+sinh2z)+(1+2sinh2z)sinhz=2sinhz+2sinh3z+sinhz+2sinh3z=3sinhz+4sinh3z
Therefore, option (C) is the correct answer.
equals