Find all solutions of the equation: 2cos^2x-cosx=1

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Solve the trigonometric equation:

     

Make a substitution:

     

and the equation becomes

     

Rewrite conveniently  – t  as  + t – 2t,  and then factor the left-hand side by grouping:

     

Factor out  2t + 1:

     

Substitute back for  t = cos x:

     

Therefore,

     

where  k  is an integer.

Solution set:   



I hope this helps. =)