Find the acute angle theta satisfying the equation cosec squared theta + cos squared theta is equal to 3
Answers
Answered by
1
Cosec² Ф + cos² Ф = 3
=> 1/sin²Ф + 1 - sin²Ф = 3
multiply by sin²Ф :
1 - sin⁴ Ф - 2 sin² Ф = 0
=> sin⁴ Ф + 2 sin² Ф- 1 = 0
=> sin² Ф = √2 - 1, ignoring the -ve value.
=> Ф ≈ 40.06°
=> 1/sin²Ф + 1 - sin²Ф = 3
multiply by sin²Ф :
1 - sin⁴ Ф - 2 sin² Ф = 0
=> sin⁴ Ф + 2 sin² Ф- 1 = 0
=> sin² Ф = √2 - 1, ignoring the -ve value.
=> Ф ≈ 40.06°
Similar questions