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prove that
sin242o - cos278o = (51/2 + 1)/8
LHS = sin242 - cos278
=-(cos278 - sin242)
we have cos2A - sin2B =cos(A+B)cos(A-B)
using this we get
LHS= -(cos120cos36)
=(cos36)/2 [ cos36 = (51/2 +1)/4 ]
=(51/2+1)/8 =RHS
hence proved
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