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prove that sin 2 42 o - cos 2 78 o = (5 1/2 + 1)/8 prove that sin242o - cos278o = (51/2 + 1)/8
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
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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