Trig2.5

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Show that \cos 40+\cos 80+\cos 160 =0\,

LHS=\cos 40+\cos 80+\cos 160\,

\cos (60-20)+\cos (60+20)+\cos (180-20)\,

\cos 60 \cos 20+\sin 60 \sin 20+\cos 60 \cos 20-\sin 60 \sin 20+\cos 180 \cos 20+\sin 180 \sin 20\,

2\cos 60 \cos 20-\cos 20\,

\cos 20-\cos 20 =0\, =RHS


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