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  1. If 2 (cos²θ– sin²θ) = 1 (θ is a positive acute angle), then cot θ is equal to
    1. - √3
    2. 1
      3
    3. 1
    4. AAAA
Correct Option: D

2(cos² θ - sin² θ) = 1

⇒ cos² θ - (1 - cos² θ) =
1
2

⇒ 2 cos² θ = 1 +
1
=
3
22

⇒ cos² θ =
3
4

⇒ sec² θ =
4
3

⇒ 1 + tan² θ =
4
3

⇒ tan² θ =
4
- 1 =
1
33

⇒ tan² θ =
1
⇒ cot θ = √3
3



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