Question

prove that sin20 sin40 sin60 sin80=3/16

Answer 1

sin 20 .sin 40.sin60.sin 80
= 3/2 . sin 20 .sin (60 - 20) sin (60+20)
= 3/2 . sin 20.(sin 2 60 - sin 2 20)
= 3/2 .sin 20 . (3/4 - sin 2 20)
= 3/8 .(3 sin 20 - 4 sin 3 20)
= 3/8 .(sin 3 . 20) = 3/8 sin 60 = 3/16

Answer 2

\[sum_{1/sqrt{n ^{2}+n}?}^{?}\] show that the sum given is 1