Question

вычислите sin(arccos 3/5+arcsin 3/5)

Answer 1

$sin(arccos frac{3}{5} +arcsinfrac{3}{5} )= \ =sin(arccos frac{3}{5} )cos(arcsinfrac{3}{5})+ cos(arccos frac{3}{5} )sin(arcsinfrac{3}{5} )= \ sin(arccos frac{3}{5} )cos(arcsinfrac{3}{5})+ frac{9}{25} = \ sqrt{1-cos^2(arccos frac{3}{5})}* sqrt{1-sin^2(arcsin frac{3}{5})}+ frac{9}{25} = \ sqrt{1- frac{9}{25}} *sqrt{1- frac{9}{25}} -frac{9}{25}=1- frac{9}{25}+frac{9}{25}=1$