prove that sin10 sin30 sin50 sin70 = 1/16

SIn10 sin30 sin50 sin70 ( since we know the value of sin 30 i.e. 1/2)

=1/2(sin10 sin50 sin70)

=1/2(sin50 sin70)sin10

=1/2(sin(60-10) sin(60+10) ) sin10

=1/2( sin squr 60 - sin squr 10) sin10

=1/2( 3/4 -sin²10) sin10

=1/8( 3 - 4sin²10 ) sin10

=1/8( 3sin10 - 4sin³10 )

=1/8( sin 3X10)

=1/16