sin2x-cos2x=(корень из 2)sin2x

Question

sin2x-cos2x=(корень из 2)sin2x

Answer 1

sqrt(2)/2*sin2x-sqrt(2)/2*cos2x=sqrt(2)*sqrt(2)/2*sin2x

sin(2x-П/4)=sin2x

 

sin2x=sqrt(1/2(1-cos4x))

sin(2x-П/4)=sqrt(1/2(1-cos(4x-П/2))

cos4x=cos(4x-П/2)=sin4x

tg4x=1

4x=П/4+Пn

x=П/16+Пn/4