Question:
cos( pi/7)cos(2pi/7)cos(4pi/7)=-(1/8)proove
Answer:
We know that cos A * cos 2A * cos 22 A * ..................* cos 2n-1 A = sin (2n A)/{2n * sin A} ...............1
Given, cos(π/7) * cos(2π/7) * cos(4π/7)
= cos(π/7) * cos(2π/7) * cos(22 π/7)
= [sin (23 * π/7) ]/{23 * sin (π/7)} .................from equation 1
= [sin (8π/7) ]/{8 * sin (π/7)}
= [sin (π + π/7) ]/{8 * sin (π/7)}
= -sin (π/7)/{8 * sin (π/7)}
= -1/8
So, cos(π/7) * cos(2π/7) * cos(4π/7) = -1/8
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