, we denote cosh‌x=t. We utilize the identity for hyperbolic functions: cosh2x−sinh2x=1 Substituting the known value, we have: ‌t2−(‌
12
5
)2=1 ‌t2−‌
144
25
=1 Solving for t2, we get: t2=‌
169
25
Thus, t=‌
13
5
. Now, we need to find sinh3x+cosh‌3‌x. We use the identities for triple angles: ‌sinh3x=3sinhx+4sinh3x ‌cosh‌3‌x=4cosh3x−3‌cosh‌x So, sinh3x+cosh‌3‌x=3sinhx+4sinh3x+4cosh3x−3‌cosh‌x We substitute the values: ‌=3(‌