1. cos 20 cos40 cos 60 cos 80=1/16



cos20 cos40 cos60 cos80= 1/16

l.h.s. :

cos20 cos40 1/2 cos80 (cos60 = 1/2)

multiply nd divide by 2

1/4 (2 cos20 cos40 cos80)

1/4 (cos(20+80)+ cos(20-80)) cos40  (2cosa cosb= cos(a+b) + cos(a-b))

1/4 (cos(-60)+ cos(100)) cos40

1/4(1/2 + cos100)cos40

1/8 cos40+ 1/4 (cos40 cos100)

multiplt nd divide by 2

2/2(1/8 cos40) + 1/8(2 cos40 cos100)

1/8 cos40+ 1/8 (cos140+ cos(-60))  (2cosa cosb= cos(a+b) cos(a-b))

1/8 cos40+ 1/8 cos140 + 1/16  (cos60= 1/2)

1/8(cos40+cos140) + 1/16

1/8(2 cos90 cos(-50)) + 1/16  (as above identity)

cos90= 0

1/16

= r.h.s

hence proved........

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