If θ is a positive acute angle and tan 2θ tan

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If θ is a positive acute angle and tan 2θ tan 3θ = 1, then the value of [2 cos² (5θ / 2) – 1[ is

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

Correct Option: C

tan2θ . tan3θ = 1

⇒ tan 3θ =	1	= cot 2θ
	tan 2θ

⇒ tan3θ = tan (90° – 2θ )
⇒ 3θ = 90° – 2θ ⇒ 5θ = 90°
⇒ θ = 18

∴ 2cos ²	5θ	- 1 = 2 cos² 45° - 1
	2