2cos^2x-1=sin3x отбор корней ** [0;П/2] помогите решить

Question

2cos^2x-1=sin3x отбор корней на [0;П/2] помогите решить

Answer 1

Cos2x=sin3x
sin3x-sin(π/2-2x)=0
2sin(5x/2-π/4)cos(x/2+π/4)=0
sin(5x/2-π/4)=0⇒5x/2-π/4=πn⇒5x/2=π/4+πn⇒x=π/10+2πn/5
cos(x/2+π/4)=0⇒x/2+π/4=π/2+πn⇒x/2=π/4+πn⇒x=π/2+2πn
x=π/10;π/2