Question

решить уравнение cos (П2-х)-sin3x+sin5x=0

Answer 1

cos(π/2-x)-sin3x+sin5x=0
sinx-sin3x+sin5x=0
2sin3x•cos2x-sin3x=0
sin3x•(2cos2x-1)=0
1)sin3x=0 => 3x=πn => x=(π/3)•n, n∊Z;
2)cos2x=½ => 2x=±π/3+2πn => x=±π/6+πn, n∊Z.