Sinx - корень 2 sin3x = -sin5x;

Question

Sinx - корень 2 sin3x = -sin5x;

Answer 1

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