cosπ/5cos2π/5cos4π/5cos8π/5=1/16.prove that
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Answer:
Step-by-step explanation:
//multiply and divide by 2sin(π/5)
=> 2sin(π/5)cos(π/5) cos(2π/5) cos(4π/5) cos(8π/5) / 2sin(π/5)
//remember 2SinACosA = Sin2A.
=> sin (2π/5)cos(2π/5) cos(4π/5) cos(8π/5) / 2sin(π/5)
//now multiply and divide by 2
=> 2sin (2π/5)cos(2π/5) cos(4π/5) cos(8π/5)/4sin(π/5)
//remember 2SinACosA = Sin2A
=> sin(4π/5)cos(4π/5) cos(8π/5)/4sin(π/5)
//now multiply and divide by 2
=> 2sin(4π/5)cos(4π/5) cos(8π/5)/8sin(π/5)
//remember 2SinACosA = Sin2A
=> sin(8π/5)cos(8π/5)/8sin(π/5)
//now multiply and divide by 2
=> 2sin(8π/5)cos(8π/5)/16sin(π/5)
//remember 2SinACosA = Sin2A
=> sin(16π/5)/16sin(π/5)
=> sin (3π + π/5) / 16sin(π/5)
=> sin(π/5)/16sin(π/5)
=> 1/16
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