Prove that cos36.cos72.cos108.cos144=1/16

Steps to prove cos36.cos72.cos108.cos144=1/16

L.H.S

=cos36.cos72.cos108.cos144

=(√5+1)/4.(√5-1)/4.cos(90+18).cos(180-36)

=(√5+1)/4[(√5-1)/4.(-sin18).(-sin36)]

=(√5+1)/4.(√5-1)/4.(√5-1)/4.(√5+1)/4

=(5-1)/16.(5-1)/16

=4/16.4/16

=1/4.1/4=1/16=R.H.S

Hence cos36.cos72.cos108.cos144=1/16 is proved.

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