If p = cosec θ – cot θ and q = (cosec θ + cot θ)-1 then which one of the following is correct?

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NDA (Held On: 21 Apr 2019) Maths Previous Year paper
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  1. p - q = 1
  2. p = q 
  3. p + q = 1
  4. p + q = 0

Answer (Detailed Solution Below)

Option 2 : p = q 
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Detailed Solution

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Concept:

cosec2 x – cot2 x = 1

Calculation:

Given: p = cosec θ – cot θ and q = (cosec θ + cot θ)-1

⇒ cosec θ + cot θ = 1/q

As we know that, cosec2 x – cot2 x = 1

⇒ (cosec θ + cot θ) × (cosec θ – cot θ) = 1

\(\frac1q \times p=1\)

⇒ p = q
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