SOLUTION: Show that cos^2 (4pi/7) - sin^2 (3pi/7) = cos 6pi/7

Question 1142056: Show that
cos^2 (4pi/7) - sin^2 (3pi/7) = cos 6pi/7
Answer by ikleyn(52903) (Show Source): You can put this solution on YOUR website!
.

First use the identity


     = ,


which gives you


     = .


Therefore, the left side of the given hypothetical identity becomes


     -  =  - .    (1)


Next, use the trigonometric identity  


    cos(a)*cos(b) - sin(a)*sin(b) = cos(a+b).


It allows you to continue the line (1) in this way


     -  =  -  =  = .


Thus 


     -  = .


It is what has to be proved.

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