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  1. If 2 (cos²θ– sin²θ) = 1, θ is a positive acute angle, then the value of θ is
    1. 60°
    2. 30°
    3. 45°
    4. 22
      1
      °
      2
Correct Option: B

2 (cos⊃θ – sin⊃θ) = 1

⇒ cosec²θ - sin²θ =
1
2

⇒ 1 - 2 sin²θ =
1
2

⇒ 2 sin²θ = 1 -
1
2

⇒ 2 sin²θ =
1
⇒ sin²θ =
1
24

⇒ sin²θ = ±
1
= sin30°
2



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