Question

Solve sinQ+ sin3Q+ sin5Q = 0

Answer 1

Sin Q + Sin 5Q + Sin 3Q = 0
2 Sin (5Q+Q)/2 Cos (5Q-Q)/2  + Sin 3Q = 0
Sin 3Q [1 + 2 Cos 2Q] = 0

    Sin 3Q = 0,  =>    3Q = n π       =>   Q = nπ/3
    Cos 2 Q = -1/2    =>   2Q = 2 m π + 2π/3 or 4π/3   
                             => Q = m π + π/3  or 2π/3 = (3m+2) π /3 ,  [3m+4]π/3

         =>  Q = n π / 3    ie.,  0, π/3 , 2π/3, π, 4π/3, 5π/3   in [0, 2π)