1) 8 cos x + 15 sin x = 17корень из 2/2 2) cos 5x*cos3x=1/2*cos 2x 3)sin 3x-sin17x=o

2)cos5x*cos3x=1/2cos2x (cos(5x-3x)+cos(5x+3x))/2=1/2cos2x cos2x+cos8x=cos2x cos8x=0 8x=π/2+πn, n∈Z x=π/16+πn/8 3)sin17x-sin3x=0 2sin(17x-3x)/2*cos(17x+3x)/2=0 2sin 14x/2*cos 20x/2=0 2sin7x*cos10x=0 sin7x=0 7x=πn, n∈Z x=πn/7 cos10x=0 10x=π/2+πn x=π/20+πn/10 1) 8cosx+15sinx=17*√2/2 8cosx+15sinx-17√/2/2=0 8cosx-17√2/2=15√(1-cos²x) 225(1-cos²x)=64cos²x-2*8*17*√2/2cosx+17²*2/4 225-225cos²x=64cos²x-136√2cosx+289/2 289cos²x-136√2cosx-161/2=0 Пусть cosx=y 289y²-136√2y-80.5=0 D=136²*2+4*80.5*289=56066 y=(136√2+-√56066)/578 x=+-arccos((136√2+-√56066)/578)+πn