Question #f1264

1 Answer
Nov 21, 2017

Please refer to the explanation below.

Explanation:

(pi/9)=20°, (2pi)/9=40°, (4pi)/9=80°

LHS=sin(pi/9)*sin((2pi)/9)*sin((4pi)/9)

=sin20°sin40°sin80°

=(2sin20°sin40°sin80°)/2

=((cos(40°-20°)-cos(40°+20°))*sin80°)/2

=((cos20°-cos60°)*sin80°)/2

=((cos20°-1/2)*sin80°)/2

=(((2cos20°-1)/2)*sin80°)/2

=((2cos20°-1)*sin80)/4

=(2cos20°sin80°-sin80°)/4

=(sin(80°+20°)+sin(80°-20°)-sin80°)/4

=(sin100°+sin60°-sin80°)/4

=(sin(180°-100°)+sin60°-sin80°)/4

=(cancel(sin80°)+sin60°cancel(-sin80°))/4

=(sqrt(3)/2)/4=sqrt(3)/8=RHS