cos ⁡ 3 x + cos ⁡ x − cos ⁡ 2 x = 0 find general solution

Question

cos  ⁡  3  x  +  cos  ⁡  x  −  cos  ⁡  2  x  =  0  find general solution

Ricardo Weiss · Accepted Answer

cos  ⁡  (  x  )  −  cos  ⁡  (  2  x  )  +  cos  ⁡  (  3  x  )  =  0  ⟺  1  −  2  cos  ⁡  (  x  )  −  2      cos    2    ⁡  (  x  )  +  4      cos    3    ⁡  (  x  )  =  0  ⟺      (    2    cos    ⁡    (    x    )    −    1    )    ⋅      (    2          cos      2        ⁡    (    x    )    −    1    )    =  0  ⟺  2  cos  ⁡  (  x  )  −  1  =  0  ⟺  ∨  2      cos    2    ⁡  (  x  )  −  1  =  0  ⟺  2  cos  ⁡  (  x  )  =  1  ⟺  ∨  2      cos    2    ⁡  (  x  )  =  1  ⟺  cos  ⁡  (  x  )  =      1    2    ⟺  ∨      cos    2    ⁡  (  x  )  =      1    2    ⟺  cos  ⁡  (  x  )  =      1    2    ⟺  ∨  cos  ⁡  (  x  )  =  ±      1          2        ⟺  cos  ⁡  (  x  )  =      1    2    ⟺  ∨  cos  ⁡  (  x  )  =      1          2        ∨  cos  ⁡  (  x  )  =  −      1          2        ⟺  x  =      π    3    +  2  π      n    1    ∨  x  =            5      π        3    +  2  π      n    2    ∨  x  =      π    4    +  2  π      n    3    ∨  x  =            7      π        4    +  2  π      n    4    ∨  x  =            3      π        4    +  2  π      n    5    ∨  x  =            5      π        4    +  2  π      n    6  With       n    1    ,      n    2    ,      n    3    ,      n    4    ,      n    5    ,      n    6    ∈      Z

find general solution cos 3x+cos x−cos 2x=0

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