Question

The value of $\sin (A+B)$ if $\sin A=\frac{3}{4}$ and $cosB=\frac{8}{17}$

Answer 1

$\sin A=\frac{3}{5}⟹\cos A=\frac{4}{5}$

$\cos B=\frac{8}{17}⟹\sin B=\frac{15}{17}$

$\sin (A+B)=\sin A\cos B+\cos A\sin B\frac{3}{5}\times \frac{8}{17}+\frac{4}{5}\times \frac{15}{17}\frac{24+60}{85}=\frac{84}{85}$