Question

cos(7x-π/8)+sin(7x-π/8)=√2. найдите х

Answer 1

$cos(7x- frac{pi}{8} )+sin (7x- frac{pi}{8})= sqrt{2}$

Формула: $asin x+bcos x = sqrt{a^2+b^2}sin(x+arcsin( frac{b}{ sqrt{a^2+b^2} } ))$

$sqrt{1^2+1^2} sin(7x- frac{pi}{8}+arcsin( frac{1}{ sqrt{1^2+1^2} } ))= sqrt{2}\ \ sqrt{2} sin (7x- frac{pi}{8}+ frac{pi}{4})= sqrt{2},, |: sqrt{2} \ \ sin(7x+ frac{pi}{8} )=1\ \ 7x+frac{pi}{8}= frac{pi}{2}+2 pi k,kin Z\ \ 7x= frac{3 pi }{8} +2pi k,k in Z\ \ x= frac{3 pi }{56} + frac{2 pi k}{7} ,k in Z$