Question

prove that cosa×cos4a×cos×8a=sin16a/16

Answer 1

Given cosA x cos2A x cos4A x cos8A = sin16A/16sinA
RHS
sin16A/16sinA
[2sin8A cos 8A]/16sinA
[cos8A(2sin4A cos4A)]/8sinA
[cos8A cos 4A(2 sin 2A cos 2A)]/4sinA
[cos 8A cos 4A cos 2A(sin2A)]/2 sinA
[cos8A cos 4A cos 2A(2sinA cos A)]/2
sin A cos A cos 2A cos 4A cos 8A
Hence RHS=LHS

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