Question

cos2π/15.cos4π/15.cos8π/15.cos16π/15=1/16​

Answer 1

Answer:

Step-by-step explanation:

Cos2π/15.cos4π/15.cos8π/15.cos16π/15

= Cos2π/15.cos4π/15.cos8π/15.cos(π+π/15)

= Cos2π/15.cos4π/15.cos8π/15cosπ/15

multiply and divide by Sinπ/15

= 1/(2Sinπ/15)[(2Sinπ/15cosπ/15)Cos2π/15.cos4π/15.cos8π/15]

= 1/(2Sinπ/15)[(Sin2π/15Cos2π/15.cos4π/15.cos8π/15)]

= 1/(4Sinπ/15)[(2Sin2π/15Cos2π/15)cos4π/15.cos8π/15]

= 1/(4Sinπ/15)[(Sin4π/15cos4π/15.cos8π/15)]

=1/(8Sinπ/15)[(2Sin4π/15cos4π/15)cos8π/15]

= 1/(8Sinπ/15)[(Sin8π/15Cos8π/15)]

= 1/(16Sinπ/15)[(2Sin8π/15Cos8π/15)]

= 1/(16Sinπ/15) * Sin16π/15

= 1/(16Sinπ/15) * Sin(π+π/15)

= 1/(16Sinπ/15) * Sinπ/15

= 1/16.

= R.H.S

Hence proved.