Grade 11Trigonometry
Cosπ/15cos2π/15cos3π/15cos4π/15cos5π/15cos6π/15cos7π/15 =?
Cosπ/15cos2π/15cos3π/15cos4π/15cos5π/15cos6π/15cos7π/15 =?
1 Answer
Arun
cos(π/15) cos(2π/15) cos(3π/15) cos(4π/15) cos(5π/15) cos(6π/15) cos(7π/15)
=sin(8π/15)cos(3π/15)cos(5π/15)cos(7π/15) cos(6π/15)/(8sinπ/15)
=[sin14π/15/(16sinπ/15)]cos(3π/15)cos(5π/15)cos(6π/15)
=(1/16)4sin3π/15cos3π/15cos6π/15/[4sin(3π/15)] cos5π/15
=(1/16)*(sin3π/15)/(4sin3π/15)cos(5π/15)
=(1/64)*(1/2)=1/128
=sin(8π/15)cos(3π/15)cos(5π/15)cos(7π/15) cos(6π/15)/(8sinπ/15)
=[sin14π/15/(16sinπ/15)]cos(3π/15)cos(5π/15)cos(6π/15)
=(1/16)4sin3π/15cos3π/15cos6π/15/[4sin(3π/15)] cos5π/15
=(1/16)*(sin3π/15)/(4sin3π/15)cos(5π/15)
=(1/64)*(1/2)=1/128
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