Solved Problems

Problem 1: Evaluate $\sinh(\ln 3)$ and $\cosh(\ln 3)$ exactly without a calculator.

Problem 2: Prove the identity $\cosh(2x) = \cosh^2 x + \sinh^2 x$ using the exponential definitions.

Problem 3: Find the exact solution to the equation $3 \sinh x + \cosh x = 2$.

Problem 4: Given $\tanh x = \frac{12}{13}$ and $x \gt 0$, find the exact values of $\cosh x$ and $\sinh x$.