4sin2x-3sin(2x-pi/2)=5

4sin2x-3sin(2x-π/2)=54sin2x+3cos2x=58sinxcosx + 3cos²x-3sin²x=5sin²x+5cos²x8sin²x-8sinxcosx+2cos²x=0|:2cos²x4tg²x-4tgx+1=0(2tgx-1)²=0tgx=1/2x=arctg(1/2) + πn,n ∈ Z

4sin2x+3cos2x=5Разделим обе части уравнения на √(4²+3²)=√(16+9)=√25=54/5*sin2x+3/5*cos2x=1sin(2x+φ)=12x+φ=π/2+2πn,n∈Z2x=π/2-φ+2πn,n∈Zx=π/4-1/2*φ+πn,n∈Zφ=arcsin3/5x=π/4-1/2*arcsin0,6+πn,n∈Z