Without using calculator, evaluate: Cos100cos120cos140cos160 ?

1 Answer
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