Question

помогите!!! sin7x+cos7x=корень из 2на sin11x

Answer 1

$sin7x+cos7x=sqrt2cos11x\ sin7x+cos7x=sqrt2(frac{sqrt2}{2}sin7x+frac{sqrt2}{2}cos7x)=\=sqrt2(sin7xcosfrac{pi}{4}+cos7xsinfrac{pi}{4})=sqrt2sin(7x+frac{pi}{4})\sin(7x+frac{pi}{4})=cos11x\cos(frac{pi}{2}-(7x+frac{pi}{4}))=cos11x\cos(frac{pi}{4}-7x)=cos11x\frac{pi}{4}-7x=pm11x+2pi k\1)frac{pi}{4}-7x=11x+2pi k\18x=frac{pi}{4}-2pi k\x=frac{pi}{72}-frac{pi}{9}k\2)frac{pi}{4}-7x=-11x+2pi k\4x=-frac{pi}{4}+2pi k\x=-frac{pi}{16}+frac{pi}{2}k$