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

$-\frac{13}{85}$

sinA = \(\frac{4}{5}\)                              sinB = \(\frac{15}{17}\) 

By using pythagoras theorem ,           By using pythagoras theorem ,

P² + B² = H²                                            P² + B² = H²                                         4² + B² = 5²                                            15² + B² = 17²

B = 3                                                           B = 8

cos A = \(\frac{3}{5}\)                    cos B = \(\frac{8}{17}\) 

sin ( A - B ) = sinA cosB - cosA sinB

= \(\frac{4}{5}\)  × \(\frac{8}{17}\)  - \(\frac{3}{5}\) × \(\frac{15}{17}\) 

= \(\frac{32}{85}\)  - \(\frac{45}{85}\) 

=  - \(\frac{13}{85}\)