Question

$sin3z-cos3z= sqrt{ frac{3}{2} }$

Answer 1

Формула $asin xpm bcos x=c \ sqrt{a^2+b^2} sin(xpmarcsin beta )=c$где $beta = frac{b}{ sqrt{a^2+b^2} }$

$sin 3z-cos 3z= sqrt{1.5} \ sqrt{a^2+b^2} = sqrt{1^2+1^2} = sqrt{2} \ sqrt{2} sin(3z- frac{ pi }{4} )= sqrt{1.5} \ sin(3z-frac{ pi }{4})= frac{ sqrt{3} }{2} \ \ 3z-frac{ pi }{4}=(-1)^kcdot frac{ pi }{3} + pi k, k in Z \ 3x=(-1)^kcdotfrac{ pi }{3}+frac{ pi }{4}+ pi k, k in Z \ \ x=(-1)^kcdot frac{ pi }{6} + frac{ pi }{12} + frac{ pi k}{3} , k in Z$