Question

COS3 TITA / 2COS 2 TITA - 1

Answer 1

=> cos θ = √{1 - (4/5)2 }

=> cos θ = √{1 - 16/25}

=> cos θ = √(9/25)

=> cos θ = 3/5

=> cos (2 * θ/2) = 3/5

=> 2cos2 θ/2 - 1 = 3/5

=> 2cos2 θ/2 = 3/5 + 1

=> 2cos2 θ/2 = 8/5

=> cos2 θ/2 = 4/5

=> cos θ/2 = √(4/5)

=> cos θ/2 = 2/√5

Again, sin θ/2 = √(1 - cos2 θ/2)

=> sin θ/2 = √[1 - √(4/5)}2 ]

=> sin θ/2 = √{1 - 4/5}

=> sin θ/2 = √(1/5)

=> sin θ/2 = 1/√5

Now, tan θ/2 = sin θ/2/cos θ/2

                   = (1/√5)/(2/√5)

                    = 1/2

Hence, tan θ/2 = 1/2