Question

Cos pi/17 cos 2 pi/17 cos 4 pi/17 cos 9 pi/17​

Answer 1

HELLO DEAR,

we know:-

• we know:- cosx . cosy = 1/2{cos(x + y) + cos(x - y)}
• 2sinx.cosx = sin2x
• sin(-∅) = -sin∅

now,

multiply and divide by 2sinπ/17.

=> {(2sinπ/17 × cosπ/17) × cos2π/17 × cos4π/17 × cos9π/17}/(2sinπ/17)

=> {(2sin2π/17 × cos2π/17) × cos4π/17 × cos9π/17}/(4sinπ/17)

=> {(2sin4π/17 × cos4π/17) × cos9π/17}/(8sinπ/17)

=> (sin8π/17 × cos9π/17)/(8sinπ/17)

=> {sin(17π/17) + sin(-π/17)}/(16sinπ/17)

=> {sinπ/17 - sinπ/17}/(16sinπ/17)

=> 0.

I HOPE IT'S HELP YOU DEAR,

THANKS