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Exercise

$\frac{e^{ax}-e^{bx}}{\sin\left(ax\right)-\sin\left(bx\right)}$

Step-by-step Solution

1

Apply the trigonometric identity: $\sin\left(a\right)-\sin\left(b\right)$$=2\sin\left(\frac{a-b}{2}\right)\cos\left(\frac{a+b}{2}\right)$, where $a=ax$ and $b=bx$

$\frac{e^{ax}-e^{bx}}{2\sin\left(\frac{ax-bx}{2}\right)\cos\left(\frac{ax+bx}{2}\right)}$

Final answer to the exercise

$\frac{e^{ax}-e^{bx}}{2\sin\left(\frac{ax-bx}{2}\right)\cos\left(\frac{ax+bx}{2}\right)}$

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