Question

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Answer 1

Answer:

Step-by-step explanation:

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

Step-by-step explanation:

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