Sinx - корень 2 sin3x = - sin5x;

Sinx+sin5x=√2sin3x

2sin ((5x+x) / 2) * cos ((5x-x) / 2=√2sin3x

2sin3x*cos2x=√2sin3x

2sin3x*cos2x-√2sin3x=0

2sin3x (cos2x-√2/2) = 0

sin3x=0

3x=πk, k∈Z

x=πk/3

cos2x-√2/2=0

cos2x=√2/2

2x=+-π/4+2πk, k∈Z

x=+-π/8+πk