| What is the double angle identity for \sinh 2x? | \sinh 2x \equiv 2 \sinh x \cdot \cosh x |
| How is \sinh x defined in terms of exponentials? | \sinh x = \frac{e^x - e^{-x}}{2} |
| How is \cosh x defined in terms of exponentials? | \cosh x = \frac{e^x + e^{-x}}{2} |
| Starting from 2 \sinh x \cdot \cosh x, what is the first step of the proof using exponential definitions? | 2\cdot\frac{e^x - e^{-x}}{2}\cdot\frac{e^x + e^{-x}}{2} |
| After simplifying 2\cdot\frac{e^x - e^{-x}}{2}\cdot\frac{e^x + e^{-x}}{2}, what expression is obtained? | \frac{(e^x - e^{-x})(e^x + e^{-x})}{2} |
| What is the result of expanding (e^x - e^{-x})(e^x + e^{-x})? | e^{2x} - e^{-2x} |
| What final expression does \frac{e^{2x} - e^{-2x}}{2} equal? | \sinh 2x |