Question

$sin( frac{x}{3} ) cos( frac{pi}{5} ) - cos( frac{x}{3} ) sin( frac{pi}{5} ) = frac{ sqrt{2} }{2}$

Answer 1

$sin( frac{x}{3} ) cos( frac{pi}{5} ) - cos( frac{x}{3} ) sin( frac{pi}{5} ) = frac{ sqrt{2} }{2}\\ sin(frac{x}{3}-frac{pi}{5})=frac{sqrt{2}}{2}\\ frac{x}{3}-frac{pi}{5}=(-1)^k*frac{pi}{4}+pi k, kin Z\\ frac{x}{3}=frac{pi}{5}+(-1)^k*frac{pi}{4}+pi k, kin Z\\ x=frac{3pi}{5}+(-1)^k*frac{3pi}{4}+3pi k, kin Z$

Ответ: $frac{3pi}{5}+(-1)^k*frac{3pi}{4}+3pi k, kin Z$