Question

Prove that :4sin18. Sin234 = -1​

Answer 1

SOLUTION

L.H.S 4sin 18× sin 234

sin 234°= sin(180°+54°)

=)sin180° cos 54° +cos 180° sin 54°

=) -sin 54°

Let x= -sin 18° × sin 54°

Then 4 cos 18°

=)- cos 18°. sin 18°. sin 54°

=)-(1/2) sin 36° cos(90°-54°)

=)-(1/2) sin 36°. cos 36°

=) -(1/4) sin 72°

=) -(1/4) cos (90°-72°)

=) -(1/4) cos 18°

so, 4 cos 18°

=)4 (-1/4) cos 18°

=) x= 4× (-1/4)

=) x= -1 R.H.S.