Question

Question #f5163

Answer 1

`LHS=sin( pi/5)sin ((2pi)/5)sin(pi-(2pi)/5)sin(pi-pi/5)`

`=sin( pi/5)sin ((2pi)/5)sin((2pi)/5)sin(pi/5)`

`=sin^2( pi/5)sin^2((2pi)/5)`

`=(sin( pi/5)sin((2pi)/5))^2`

`=((sqrt(10-2sqrt5)/4)(sqrt(10+2sqrt5)/4))^2`

`=(100-20)/256=80/256=5/16`

Proved