Question

Упростить выражение $\frac{sin(a+b)-sinb*cosa}{sin(a-b)+sinb*cosa}$

Answer 1

sin(a+b) ≡ sin(a)cos(b) + sin(b)cos(a)

sin(a-b) ≡ sin(a)cos(b) - sin(b)cos(a)

$\frac{\sin(a+b) - \sin(b)\cdot\cos(a)}{\sin(a-b) + \sin(b)\cdot\cos(a)} \equiv$

$\equiv \frac{\sin(a)\cos(b)}{\sin(a)\cos(b)} \equiv 1$