If y = sec2 θ + cos2 θ, where , then which one of the following is correct?  

  1. y = 0
  2. 0 ≤ y ≤ 2
  3. y ≥ 2
  4. None of the above

Answer (Detailed Solution Below)

Option 3 : y ≥ 2
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Detailed Solution

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Concept:

Trigonometric Property :

Calculations:

Given, y = sec2 θ + cos2 θ, where 

⇒ y = sec2 θ + cos2 θ - 2 + 2

⇒ y = sec2 θ - 2 sec θ cos θ + cos2 θ + 2

⇒ y = (sec - cos θ)2 + 2

As (sec - cos θ) 0

⇒ (sec - cos θ)2 + 2 ​ 2

⇒ y ≥ 2

Hence, if y = sec2 θ + cos2 θ, where , then y ≥ 2

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