Question

cos(arccos(3/5)+arcsin(8/17))

Answer 1

$cos(arccos frac{3}{5}+arcsin frac{8}{17})=\\=cos(arccos frac{3}{5})cdot cos(arcsin frac{8}{17})-sin(arccosfrac{3}{5})cdot sin(arcsinfrac{8}{17})=\\= frac{3}{5} cdot frac{sqrt{17^2-8^2}}{17} - frac{sqrt{5^2-3^2}}{5} cdot frac{8}{17}= frac{3}{5} cdot frac{15}{17}- frac{4}{5} cdot frac{8}{17}= frac{13}{85}$