Question

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

Answer 1

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