Тригонометрия
sin $frac{x}{3}cos frac{p}{5}-cos frac{x}{3}sin frac{p}{5}= frac{sqrt{2} }{2}$

$sin(frac{x}{3}-frac{pi}{5})=frac{sqrt{2}}{2}$
1) $frac{x}{3}-frac{pi}{5}=frac{ pi }{4}+2 pi k$
$frac{x}{3}=frac{pi}{4}+frac{pi}{5}+2 pi k$
$frac{x}{3}=frac{9pi}{20}+2 pi k$
$x=frac{27pi}{20}+6 pi k$

2) $frac{x}{3}-frac{pi}{5}=frac{3pi }{4}+2 pi k$
$frac{x}{3}=frac{3pi }{4}+frac{pi}{5}+2 pi k$
$frac{x}{3}=frac{19pi }{20}+2 pi k$
$x=frac{57pi }{20}+6 pi k$