sin ⁡ x ⋅ sin ⁡ 2 x ⋅ sin ⁡ 3 x = sin ⁡ 4 x 4 - solving a trigonometric equation

Question

sin  ⁡      x    ⋅  sin  ⁡      2    x    ⋅  sin  ⁡      3    x    =            sin      ⁡              4        x              4   - solving a trigonometric equation

Turynka2f · Accepted Answer

sin  ⁡      x    ⋅  sin  ⁡      2    x    ⋅  sin  ⁡      3    x    =            2      ⋅      sin      ⁡              2        x            ⋅      cos      ⁡      2      x        4    2  ⋅  sin  ⁡      x    ⋅  sin  ⁡      2    x    ⋅  sin  ⁡      3    x    =  sin  ⁡      2    x    ⋅  cos  ⁡  2  x  sin  ⁡  2  x  (  2  ⋅  sin  ⁡      x    ⋅  sin  ⁡      3    x    −  cos  ⁡  2  x  )  =  0  sin  ⁡  2  x  (  −  cos  ⁡  4  x  +  cos  ⁡  2  x  −  cos  ⁡  2  x  )  =  0  ⇒  sin  ⁡  2  x  ⋅  cos  ⁡  4  x  =  0  sin  ⁡  2  x  =  0  ⇒  x  =            k      π        2    cos  ⁡  4  x  =  0  ⇒  x  =      π    8    +            k      π        4

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