Question

Prove that : 16 cosπ/15 cos2π/15 cos4π/15 cos 8π/15 = -1​

Answer 1

Answer:

cos(2π/15)+cos(4π/15)+cos(8π/15)+cos(16π/15)

=2cos(9π/15)cos(7π/15)+2cos(6π/15)cos(6π/15)cos(2π/15)

=2cos(3π/5)*[cos(7π/15)-cos(2π/15)]

=-4cos(3π/5)sin(3π/10)sin(π/6)

=-2cos(3π/5)sin(3π/10)