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=1/2cos2xcos2x+cos8x=cos2xcos8x=08x=π/2+πn, n∈Zx=π/16+πn/83)sin17x-sin3x=02sin(17x-3x)/2*cos(17x+3x)/2=02sin 14x/2*cos 20x/2=02sin7x*cos10x=0sin7x=07x=πn, n∈Zx=πn/7cos10x=010x=π/2+πnx=π/20+πn/101) 8cosx+15sinx=17*√2/28cosx+15sinx-17√/2/2=08cosx-17√2/2=15√(1-cos²x)225(1-cos²x)=64cos²x-2*8*17*√2/2cosx+17²*2/4225-225cos²x=64cos²x-136√2cosx+289/2289cos²x-136√2cosx-161/2=0Пусть cosx=y289y²-136√2y-80.5=0D=136²*2+4*80.5*289=56066y=(136√2+-√56066)/578x=+-arccos((136√2+-√56066)/578)+πn