SOLUTION: What is the value of cos(2α) , if 2 cos(3α)= cos(α)?

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Question 1126751: What is the value of cos(2α) , if 2 cos(3α)= cos(α)?
Answer by ikleyn(52788)   (Show Source): You can put this solution on YOUR website!
.
Start from this basic identity


    cos(3a)=4*cos^3(a) - 3*cos(a).


Then 2*cos(3a) = 8*cos^3(a) - 6*cos(a),  and we are given that


    8*cos^3(a) - 6*cos(a) = cos(a).


It implies


     = 0.


So, either  cos(a) = 0   or    = 0;  the last is equivalent to   = .


Case 1.  If  cos(a) = 0,  then  cos(2a) =  = -1.


Case 2.  If   = ,  then  cos(2a) =  =  =  =  = .


Answer.  If  2*cos(3a) = cos(a),  then EITHER  cos(2a) = -1  OR  cos(2a) = .

Solved.


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