Without using calculator, evaluate: Cos100cos120cos140cos160 ?

1 Answer
P dilip_k
May 15, 2017

#cos100cos120cos140cos160#

#=cos(180-80)cos(180-60)cos(180-40)cos(180-20)#

#=(-cos80)(-cos60)(-cos40)(-cos20)#

#=cos20xxcos40xxcos80cos60#

#=1/(8sin20)xx4*2sin20xxcos20xxcos40xxcos80cos60#

#=1/(8sin20)xx2*2sin40xxcos40xxcos80cos60#

#=1/(8sin20)xx2sin80xxcos80cos60#
#=1/(8sin20)xxsin160cos60#

#=1/(8sin20)xxsin(180-20)xx1/2#

#=1/(16sin20)xxsin20=1/16#

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