Question

cos pie/11cos 2pie/11 cos 3pie/11cos 4pie/11cos5pie/11=1/32​

Answer 1

Answer:

1/32

Step-by-step explanation:

Given :

cos(π/11) * cos(2π/11) * cos(3π/11) * cos(4π/11) * cos(5π/11)

Multiply and divide by 2 sin(π/11)

⇒ [2 sin(π/11)/ 2 sin π/11] * cos(π/11) * cos(2π/11) * cos(π - 8π/11) * cos(4π/11) * cos(5π/11)

⇒ [-2sin(2π/11) * cos(2π/11) / 2 sin(π/11) * 2] * cos(8π/11) * cos(4π/11) * cos(5π/11)

⇒ [(-2 sin 4π/11) * cos(4π/11) * cos(8π/11) * cos(5π/11)]/4 sin(π/11) * 2

⇒ [-2 sin(8π/11) * cos(8π/11) * cos(5π/11)]/[8 sin (π/11) * 2]

⇒ [-sin(16π/11) * cos(5π/11)]/[(16 sin(π/11)]

⇒ [-sin(π + 5π/11) * cos(5π/11)]/[(16 sin(π/11)]

⇒ [2 sin (5π/11) * cos(5π/11)]/[(16 sin(π/11) * 2]

⇒ [sin(10π/11)]/[32 sin(π/11)]

⇒ [sin(π - π/11)]/[32 sin(π/11)]

⇒ [sin(π/11])/[32 sin(π/11)]

⇒ 1/32

Hope it helps!