Question

PLZ. EXPLAIN IT

cos 2pi/15. cos 4pi/15. cos 8pi/15. cos 16pi/15 = 1/16 , how??? and also answer my previous question

Answer 1

To Prove :cos 2pi/15. cos 4pi/15. cos 8pi/15. cos 16pi/15 = 1/16

Let L.H.S be  cos 2π/15. cos 4π/15. cos 8π/15. cos 16π/15

cos 2π/15=cos (2x180)/15=cos(360/15)=cos24°

Similarly : cos 4π/15.=Cos48°

 cos 8π/15=cos 96°


cos 16π/15=Cos 192°

∴L.H.S =cos24°Cos48°cos 96° Cos 192°
Multiply and Divide the equation by 16 sin24°

⇒(1/16 sin24°)[(2sin24°cos24°)(2Cos48°)(2cos 96°)(2 Cos 192°)]

⇒(1/16 sin24°)[Sin48°(2Cos48°)(2cos 96°)(2 Cos 192°)]  [∵Sin2A=2sinACosA]

⇒(1/16 sin24°)[(2Sin48°Cos48)(2cos 96°)(2 Cos 192°)]

⇒(1/16 sin24°)([2sin96°cos96°)((2 Cos 192°)]

⇒(1/16 sin24°)([2sin192°Cos 192°)]

⇒(1/16 sin24°)[sin384°]

⇒sin384°/16 Sin 24°

⇒Sin(360+24)/16sin24°

⇒Sin24°/16 sin24°

⇒1/16

L.H.S=R.H.S

Hence proved 

Answer 2

To find out the answer of this question I suggest u an easy method

U must remember this result first:

Cosα.cos2α.cos(2²α).cos(2³α).................cos(2^n-1 × α) = sin(2^n × α)/2^n ×sinα

ATQ,

Cos2π/15 . Cos 4π/15 . Cos4π/15 . Cos16π/15

Here,

n = 4

α = 2π/15

= (sin 2^4 × 2π/15) / (2^4 × sin2π/15)

= (sin × 32π/15) / (16 × sin 2π/15)

= sin (2π + 2π/15) / (16 × sin 2π/15)

= (sin 2π/15) / (16 × sin 2π/15)

Sin 2π/15 gets cancelled

= 1/16

Hence proved

Please mark me BRAINLIEST for telling a RESULT.