show that cos x.cos 2x.cos 4x.cos 8x = sin(2⁴x)/2⁴sin X ,if sin x ≠ 0.
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Answer:
LHS= 1/2sinx[(2sinxcosx)cos2xcos4xcos8x]
=1/2sinx(sin2xcos2xcos4xcos8x)
=1/4sinx[(2sin2xcos2x)cos4xcos8x]
=1/8sinx[(2sin4xcos4x)cos8x]
=1/8sinx(sin8xcos8x)
=1/16sinx(2sin8xcos8x)
=1/16sinx(sin16x)
=sin16x/sin16x
RHS=sin(2^4x)/2^4sinx
=sin16x/sin16x
So, LHS=RHS
Hence Proved
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