If sec θ – cos θ = (3 / 2) where θ is

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If sec θ – cos θ = (3 / 2) where θ is a positive acute angle, then the value of secθ is

1. - 1
  2
2. 1
3. 2
4. 0

Correct Option: C

secθ – cosθ =	3
	2

⇒ secθ –	1	=	3
	secθ		2

⇒	sec²θ – 1	=	3
	secθ		2

⇒ 2sec²θ – 2 = 3 secθ
⇒ 2 sec²θ – 3 secθ – 2 = 0
⇒ 2 sec²θ – 4 secθ + secθ – 2 = 0
⇒ 2 secθ (secθ – 2) + 1 (secθ – 2) = 0
⇒ (2 secθ + 1) (secθ – 2) = 0
⇒ secθ = 2 because 2 secθ + 1 ≠ 0
θ is positive acute angle.