Question

Решить уравнения:
$(1+ sqrt{2} cos x)(1-4sinxcosx)=0$
$(1- sqrt{2} cos x)(1+2sin2xcos2x)=0$

Answer 1

$(1+ sqrt{2} cos x)(1-4sinxcosx)=0 \ (1+ sqrt{2} cos x)(1-2sin2x)=0 \ left { {{1+ sqrt{2} cos x=0} atop {1-2sin2x=0}} right. \ left { {{cos x=- frac{ sqrt{2}}{2} } atop {sin2x= frac{1}{2} }} right. \ left { {{x=pm frac{ 3pi}{4}+2pi n } atop {2x=(-1)^k frac{pi}{6}+pi k }} right. \ left { {{x=pm frac{ 3pi}{4}+2pi n , nin Z} atop {x=(-1)^k frac{pi}{12}+ frac{pi k }{2}, kin Z }} right.$$(1- sqrt{2} cos x)(1+2sin2xcos2x)=0 \ (1- sqrt{2} cos x)(1+sin4x)=0 \ left { {{1- sqrt{2} cos x=0} atop {1+sin4x=0}} right. \ left { {{cos x= frac{ sqrt{2} }{2} } atop {sin4x=-1}} right. \ left { {{x=pm frac{ pi}{4}+2pi n } atop {4x=- frac{pi}{2}+2pi n }} right. \ left { {{x=pm frac{ pi}{4}+2pi n , nin Z } atop {x=- frac{pi}{8}+ frac{pi n}{2}, nin Z }} right.$