Question

sin20°sin40°sin60°sin80°=3/16

Answer 1

Hey !!!

from LHS

sin20° sin40° sin60° sin80°

sin60° sin20 sin40° sin80°

√3/2 sin20° sin40° sin80°

we know a defined rule ⚜

sinx sin ( 60° - x ) sin ( 60° + x) =
$\boxed{ \frac{1}{4} sin3x}$

similarly

hence,

let x = 20 °

then

= √3/2 × 1/4sin 3*20°

= √3/2 ×1/4sin60°

√3/2*√3/2 ×1/4


= 3/16 LHS = RHS prooved ♻

_____________________________

Hope it helps you !!!!

$\underline{rajukumar111}$

Answer 2

sin80=sin[90-10]=cos10
sin60=sin[90-30]=cos30

sin20sin40cos10cos30

we have an identity

sin∅×cos∅=1

so answer is 1