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Consider an equilateral triangle ....with length let say "a"....
now construct  a medium through one of the vertex which divide the base in two halves ........so now  length of base is a/2...........ok?
now cos= base/hypotenuse
our base is a/2
and length of hypotenuse is a ......(equilateral triangle)
so dividing them we get cos(60)=(a/2a)........(.in equilateral triangle all angle are equal to 60 )
a and a get cancel out so we get

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