sec⁡θ=a2+b2a2−b2, where a,b,∈R, gives real values of θ if and only if

secθ=a2+b2a2b2, where a,b,R, gives real values of θ if and only if

  1. A

    a=b0

  2. B

    |a||b|0

  3. C

    a+b=0,a0

  4. D

    none of these

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    Solution:

    Clearly,

    a2+b2a2b2 for all ||a||b∣≠0,

     a2+b2a2b21 or. a2+b2a2b21

     secθ=a2+b2a2b2 is meaningful.

    Thus, secθ=a2+b2a2b2 gives real values of θ if and only |a||b|0

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