cos(π11)cos(2π11)cos(3π11)cos(4π11)cos(5π11)
=4sin(π11)cos(π11)cos(2π11)cos(3π11)cos(4π11)cos(5π11)4sin(π11)
=2sin(4π11)cos(4π11)cos(π−8pi11)cos(5π11)8sin(π11)
=−2sin(8π11)cos(8π11)cos(5π11)16sin(π11)
=−2sin(16π11)cos(5π11)32sin(π11)
=−2sin(π+5pi11)cos(5π11)32sin(π−π11)
=sin(10π11)32sin(10π11)
=132
Explanation of steps
Multiplyig both numerator and denominator by 4sin(π11)
Applying identity 2sinAcosA=sin2A