Question

Prove that 4 cos 12 degrees × cos 48 degrees × cos 72 degrees = cos 36 degrees.

Answer 1

LHS
=4cos12°×cos48°×cos72°
=(2cos48°cos12°)×2cos72°
=[cos(48°+12°)+cos(48°-12°)]×2cos72°  [2cosAcosB=cos(A+B)+cos(A-B)]
=(cos60°+cos36°)×2cos72°
=1/2×2cos72°+2cos72°cos36°
=cos72°+[cos(72°+36°)+cos(72°-36°)]
=cos72°+cos108°+cos36°
=2cos(108°+72°)/2cos(108°-72°)/2+cos36°   [cosC+cosD=2cos(C+D)/2cos(C-D)/2]
=2cos(180°/2)cos(36°/2)+cos36°
=2cos90°cos18°+cos36°
=2×0×cos18°+cos36°
=cos36°=RHS (Proved)

Answer 2

hope this helps you...

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