Cosπ/11cos2π/11cos3π/11cos4π/11cos5π/11=1/32
Answers
Answer:
Step-by-step explanation:
Cosπ/11cos2π/11cos3π/11cos4π/11cos5π/11
//multiply and divide by 2sinπ/11
=> (2Sinπ/11Cosπ/11)cos2π/11cos3π/11cos4π/11cos5π/11 / 2Sinπ/11
=> Sin2π/11cos2π/11cos3π/11cos4π/11cos5π/11 / 2Sinπ/11
//multiply and divide by 2
=> (2Sin2π/11cos2π/11)cos3π/11cos4π/11cos5π/11 / 4Sinπ/11
=> Sin4π/11cos3π/11cos4π/11cos5π/11 / 4Sinπ/11
//multiply and divide by 2
=> (2Sin4π/11cos4π/11)cos3π/11cos5π/11 / 8Sinπ/11
=> Sin8π/11cos3π/11cos5π/11 / 8Sinπ/11
//Sin8π/11 = Sin (π - 3π/11) = Sin3π/11
=> Sin3π/11cos3π/11cos5π/11 / 8Sinπ/11
//Multiply and divide by 2
=> (2Sin3π/11cos3π/11)cos5π/11 / 16Sinπ/11
=> Sin6π/11Cos5π/11 / 16Sinπ/11
//Cos5π/11 = Cos (π - 6π/11) = - Cos6π/11
=> Sin6π/11(- Cos6π/11) / 16Sinπ/11
//Multiply and divide by 2
=> - (2Sin6π/11Cos6π/11) / 32Sinπ/11
=> - Sin12π/11 / 32Sinπ/11
//Sin12π/11 = Sin(π + π/11) = - Sinπ/11
=> - ( - Sinπ/11) / 32Sinπ/11
=> Sinπ/11 / 32Sinπ/11
=> 1/32
= R.H.S
Hence proved.