If sinA = $$\frac{4}{5}$$ and sinB = $$\frac{{15}}{{17}},$$ what is the value of sin(A - B)?

Solution (By Examveda Team)

$$\eqalign{ & \sin A = \frac{4}{5},\,\cos A = \frac{3}{5} \cr & \sin B = \frac{{15}}{{17}},\,\cos B = \frac{8}{{17}} \cr & \sin \left( {A - B} \right) \cr & = \sin A.\cos B - \cos A.\sin B \cr & = \frac{4}{5} \times \frac{8}{{17}} - \frac{3}{5} \times \frac{{15}}{{17}} \cr & = \frac{{32}}{{85}} - \frac{{45}}{{85}} \cr & = - \frac{{13}}{{85}} \cr} $$