16sin20.sin40.sin60.sin80=3 Prove.?

1 Answer
Cem Sentin
Mar 5, 2018

Explanation in below

Explanation:

#x=16sin20*sin40*sin60*sin80#

=#16*(sqrt3)/2*sin80*sin40*sin20#

=#8sqrt3*sin80*sin40*sin20#

=#4sqrt3*(cos40-cos120)*sin20#

=#4sqrt3*(cos40+cos60)*sin20#

=#4sqrt3*cos40*sin20+4sqrt3*cos60-sin20#

=#2sqrt3*(sin60-sin20)+2sqrt3*sin20#

=#2sqrt3*sin60#

=#2sqrt3*(sqrt3)/2#

=#3#

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