Question

The value of $\cos (A-B)$ if $\sin A=\frac{3}{5}$ and $cosB=\frac{8}{17}$

Answer 1

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

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

$\cos (A-B)=\cos A\cos B+\sin A\sin B$

$=\frac{4}{5}\times \frac{8}{17}+\frac{3}{5}\times \frac{15}{17}$

$\Rightarrow \frac{32+45}{85}=\frac{77}{85}$