2cos^2x-1=sin3x отбор корней на [0; п/2] решить - вопрос №3507464221302 от gea99 01.01.2022 18:01

Question

Алгебра: 2cos^2x-1=sin3x отбор корней на [0; п/2] решить

gea99 · Answer

Cos2x=sin3xsin3x-sin(π/2-2x)=02sin(5x/2-π/4)cos(x/2+π/4)=0sin(5x/2-π/4)=0⇒5x/2-π/4=πn⇒5x/2=π/4+πn⇒x=π/10+2πn/5cos(x/2+π/4)=0⇒x/2+π/4=π/2+πn⇒x/2=π/4+πn⇒x=π/2+2πnx=π/10;π/2...