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What is (1 + cot θ - cosec θ)(1 + tan θ + sec θ) equal to?
1. 4
2. 3
3. 2
4. 1

1 Answer

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Correct Answer - Option 3 : 2

Formula used:

  • sin θ/cos θ = tan θ 
  • cos θ/sin θ = cot θ 
  • sin2θ + cos2θ = 1
  • cosec θ = 1/sin θ
  • sec θ = 1/cos θ
  • (a - b)2 = a2 - 2ab + b2

 

Calculation:

Let the required value be x.

⇒ x = (1 + cot θ - cosec θ)(1 + tan θ + sec θ)

⇒ x = (1 + cosθ/sinθ - 1/sinθ)(1 + sinθ/cosθ + 1/cosθ)

⇒ x = (sinθ + cosθ - 1)(cosθ + sinθ + 1)/(sinθ.cosθ)

⇒ x = [(sin θ + cosθ)2 - 1]/(sinθ.cosθ)

⇒ x = [sin2θ + cos2θ + 2sinθ.cosθ - 1]/(sinθ.cosθ)

(1 + cot θ - cosec θ)(1 + tan θ + sec θ) = 2

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