prove that :- 2cos π/13cos9π/13+cos3π/13+cos5π/13=0
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2cos pi/13 cos 9pi/13+ cos 3pi/13 +cos 5pi/13
=cos 10 pi/13 +cos 8 pi/13 +cos 3pi/13 +cos 5pi/13
=cos 10 pi/13 +cos 3pi/13 +cos 8pi/13 +cos 5pi/13
=2 cos pi/2 .cos 7 pi/26 +2 cos pi/2 .cos 3 pi /26
=2 (0)cos 7 pi /26 + 2(0) cos 3pi/26
=0 =R.H.S.
=cos 10 pi/13 +cos 8 pi/13 +cos 3pi/13 +cos 5pi/13
=cos 10 pi/13 +cos 3pi/13 +cos 8pi/13 +cos 5pi/13
=2 cos pi/2 .cos 7 pi/26 +2 cos pi/2 .cos 3 pi /26
=2 (0)cos 7 pi /26 + 2(0) cos 3pi/26
=0 =R.H.S.
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